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Write an equation for the line containing the indicated points.
(-6,-6) and (-3,1)
1 solutions
Answer 91483 by jim_thompson5910(28593)   on 2008-02-04 16:35:05 (Show Source):
You can put this solution on YOUR website!
| Solved by pluggable solver: Finding the Equation of a Line |
First lets find the slope through the points ( ,) and ( , )
 Start with the slope formula (note: ( , ) is the first point (,) and ( , ) is the second point (,))
 Plug in  , , , (these are the coordinates of given points)
 Subtract the terms in the numerator  to get  . Subtract the terms in the denominator  to get 
So the slope is
------------------------------------------------
Now let's use the point-slope formula to find the equation of the line:
------Point-Slope Formula------
 where  is the slope, and (,) is one of the given points
So lets use the Point-Slope Formula to find the equation of the line
 Plug in , , and (these values are given)
 Rewrite  as 
 Rewrite  as 
 Distribute 
 Multiply and  to get  . Now reduce to get 
 Subtract from both sides to isolate y
 Combine like terms and to get 
------------------------------------------------------------------------------------------------------------
Answer:
So the equation of the line which goes through the points (,) and (,) is:
The equation is now in  form (which is slope-intercept form) where the slope is and the y-intercept is 
Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver)
 Graph of through the points (,) and (,)
Notice how the two points lie on the line. This graphically verifies our answer.
|
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Graphs/124727: Please help solve:
-2x+3y=-2
y=3x-3
1 solutions
Answer 91435 by jim_thompson5910(28593) on 2008-02-03 23:07:05 (Show Source):
You can put this solution on YOUR website!
Start with the given system
 Plug in into the first equation. In other words, replace each  with  . Notice we've eliminated the variables. So we now have a simple equation with one unknown.
 Distribute
 Combine like terms on the left side
 Add 9 to both sides
 Combine like terms on the right side
 Divide both sides by 7 to isolate x
 Divide
Now that we know that , we can plug this into to find
 Substitute for each 
 Simplify
So our answer is and which also looks like )
Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer.
 Graph of (red) and (green)
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Graphs/124725: graph the line with the slope 2/3 passing through the point (-2,1)
1 solutions
Answer 91433 by jim_thompson5910(28593) on 2008-02-03 22:56:35 (Show Source):
You can put this solution on YOUR website!
If you want to find the equation of line with a given a slope of  which goes through the point (  , ), you can simply use the point-slope formula to find the equation:
---Point-Slope Formula---
where is the slope, and ) is the given point
So lets use the Point-Slope Formula to find the equation of the line
 Plug in  ,  , and  (these values are given)
 Rewrite  as 
 Distribute
 Multiply and  to get 
 Add 1 to both sides to isolate y
 Combine like terms and to get (note: if you need help with combining fractions, check out this solver)
------------------------------------------------------------------------------------------------------------
Answer:
So the equation of the line with a slope of which goes through the point ( , ) is:
which is now in form where the slope is and the y-intercept is 
Notice if we graph the equation and plot the point ( , ), we get (note: if you need help with graphing, check out this solver)
 Graph of through the point (,)
and we can see that the point lies on the line. Since we know the equation has a slope of and goes through the point (,), this verifies our answer.
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Graphs/124724: graph the inequality
3x-4y>-32
1 solutions
Answer 91432 by jim_thompson5910(28593) on 2008-02-03 22:55:56 (Show Source):
You can put this solution on YOUR website!In order to graph  , we need to graph the equation  (just replace the inequality sign with an equal sign).
So lets graph the line (note: if you need help with graphing, check out this solver)
 graph of
Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point
Substitute (0,0) into the inequality
 Plug in  and
 Simplify
(note: for some reason, some of the following images do not display correctly in Internet Explorer. So I recommend the use of Firefox to see these images.)
Since this inequality is true, we simply shade the entire region that contains (0,0)
 Graph of with the boundary (which is the line in red) and the shaded region (in green)
(note: since the inequality contains a greater-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)
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Graphs/124722: graph the line with the slope -4 ppassing through the point (2,-1)
1 solutions
Answer 91430 by jim_thompson5910(28593) on 2008-02-03 22:54:23 (Show Source):
You can put this solution on YOUR website!
If you want to find the equation of line with a given a slope of  which goes through the point ( ,  ), you can simply use the point-slope formula to find the equation:
---Point-Slope Formula---
where is the slope, and is the given point
So lets use the Point-Slope Formula to find the equation of the line
 Plug in  ,  , and  (these values are given)
 Rewrite  as 
 Distribute
 Multiply and to get
 Subtract 1 from both sides to isolate y
 Combine like terms and to get
------------------------------------------------------------------------------------------------------------
Answer:
So the equation of the line with a slope of which goes through the point ( , ) is:
which is now in form where the slope is and the y-intercept is 
Notice if we graph the equation and plot the point ( , ), we get (note: if you need help with graphing, check out this solver)
 Graph of through the point (,)
and we can see that the point lies on the line. Since we know the equation has a slope of and goes through the point (,), this verifies our answer.
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Graphs/124720: Graph f(x) = 3x + 2.
THIS IS REALLY GIVING ME PROBLEMS TRYING TO GRAPH THIS EQUASTION.
1 solutions
Answer 91422 by jim_thompson5910(28593) on 2008-02-03 22:21:43 (Show Source):
You can put this solution on YOUR website!
Looking at  we can see that the equation is in slope-intercept form where the slope is  and the y-intercept is 
Since this tells us that the y-intercept is ) .Remember the y-intercept is the point where the graph intersects with the y-axis
So we have one point
Now since the slope is comprised of the "rise" over the "run" this means
Also, because the slope is , this means:
which shows us that the rise is 3 and the run is 1. This means that to go from point to point, we can go up 3 and over 1
So starting at , go up 3 units
and to the right 1 unit to get to the next point )
Now draw a line through these points to graph
 So this is the graph of through the points and
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Graphs/124718: Solve the system by graphing.
x – 2y = 8
x + y = –1
REALLY NEED HELP GRAPHING!
1 solutions
Answer 91419 by jim_thompson5910(28593) on 2008-02-03 22:18:38 (Show Source):
You can put this solution on YOUR website!
Start with the given system of equations:
In order to graph these equations, we need to solve for y for each equation.
So let's solve for y on the first equation
Start with the given equation
 Subtract  from both sides
 Rearrange the equation
 Divide both sides by
 Break up the fraction
 Reduce
Now lets graph (note: if you need help with graphing, check out this solver)
 Graph of
So let's solve for y on the second equation
Start with the given equation
 Subtract from both sides
 Rearrange the equation
 Divide both sides by
 Break up the fraction
 Reduce
Now lets add the graph of to our first plot to get:
 Graph of (red) and (green)
From the graph, we can see that the two lines intersect at the point ( , ) (note: you might have to adjust the window to see the intersection)
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Graphs/124717: Solve the system by substitution.
2x – 4y = 18
y = –x – 12
1 solutions
Answer 91418 by jim_thompson5910(28593) on 2008-02-03 22:17:28 (Show Source):
You can put this solution on YOUR website!Start with the given system
 Plug in into the first equation. In other words, replace each with  . Notice we've eliminated the variables. So we now have a simple equation with one unknown.
 Distribute
 Combine like terms on the left side
 Subtract 48 from both sides
 Combine like terms on the right side
 Divide both sides by 6 to isolate x
 Divide
Now that we know that , we can plug this into  to find
 Substitute  for each
 Simplify
So our answer is and which also looks like )
Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer.
 Graph of (red) and (green)
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decimal-numbers/124702: write 1/300 using sientifc notation.
i feel stupid for this but oh well.
1 solutions
Answer 91416 by jim_thompson5910(28593) on 2008-02-03 22:12:15 (Show Source):
You can put this solution on YOUR website!First divide  to get 0.00333333333333 which rounds to 0.0033
 Place a decimal between the first digit 3 and the second digit 3.
Now how many spots to the left must the decimal move to go from the number to the number  ?
The decimal needs to move 3 places to the left. So this is equivalent to multiplying by  to move the decimal 3 places to the left. Notice how the exponent -3 corresponds to the number of spots the decimal needs to move.
So putting all of this information together, we get
This means that the number in scientific notation is
In other words, 
So this also means that the approximate value for is
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Graphs/124698: Solve the system by graphing.
x – 2y = 8
x + y = –1
1 solutions
Answer 91414 by jim_thompson5910(28593) on 2008-02-03 22:02:47 (Show Source):
You can put this solution on YOUR website!
Start with the given system of equations:
In order to graph these equations, we need to solve for y for each equation.
So let's solve for y on the first equation
Start with the given equation
Subtract from both sides
Rearrange the equation
Divide both sides by
Break up the fraction
Reduce
Now lets graph (note: if you need help with graphing, check out this solver)
Graph of
So let's solve for y on the second equation
Start with the given equation
Subtract from both sides
Rearrange the equation
Divide both sides by
Break up the fraction
Reduce
Now lets add the graph of to our first plot to get:
Graph of (red) and (green)
From the graph, we can see that the two lines intersect at the point ( , ) (note: you might have to adjust the window to see the intersection)
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Graphs/124711: graph the inequality
2x+y<-9
1 solutions
Answer 91413 by jim_thompson5910(28593) on 2008-02-03 21:59:51 (Show Source):
You can put this solution on YOUR website!In order to graph  , we need to graph the equation  (just replace the inequality sign with an equal sign).
So lets graph the line (note: if you need help with graphing, check out this solver)
 graph of
Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point
Substitute (0,0) into the inequality
 Plug in and
 Simplify
(note: for some reason, some of the following images do not display correctly in Internet Explorer. So I recommend the use of Firefox to see these images.)
Since this inequality is not true, we do not shade the entire region that contains (0,0). So this means we shade the region that is on the opposite side of the line
 Graph of with the boundary (which is the line in red) and the shaded region (in green)
(note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)
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Graphs/124710: graph the inequality
-x-y<8
1 solutions
Answer 91412 by jim_thompson5910(28593) on 2008-02-03 21:58:50 (Show Source):
You can put this solution on YOUR website!In order to graph  , we need to graph the equation  (just replace the inequality sign with an equal sign).
So lets graph the line (note: if you need help with graphing, check out this solver)
 graph of
Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point
Substitute (0,0) into the inequality
 Plug in and
 Simplify
(note: for some reason, some of the following images do not display correctly in Internet Explorer. So I recommend the use of Firefox to see these images.)
Since this inequality is true, we simply shade the entire region that contains (0,0)
 Graph of with the boundary (which is the line in red) and the shaded region (in green)
(note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)
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Graphs/124709: graph the line with slope 4 passing through the point (4,2)
1 solutions
Answer 91411 by jim_thompson5910(28593) on 2008-02-03 21:57:52 (Show Source):
You can put this solution on YOUR website!
If you want to find the equation of line with a given a slope of  which goes through the point ( , ), you can simply use the point-slope formula to find the equation:
---Point-Slope Formula---
where is the slope, and is the given point
So lets use the Point-Slope Formula to find the equation of the line
 Plug in  ,  , and  (these values are given)
 Distribute
 Multiply and to get 
 Add 2 to both sides to isolate y
 Combine like terms and to get 
------------------------------------------------------------------------------------------------------------
Answer:
So the equation of the line with a slope of which goes through the point ( , ) is:
which is now in form where the slope is and the y-intercept is 
Notice if we graph the equation and plot the point ( , ), we get (note: if you need help with graphing, check out this solver)
 Graph of through the point (,)
and we can see that the point lies on the line. Since we know the equation has a slope of and goes through the point (,), this verifies our answer.
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Equations/124706: t/9-7=-5
1 solutions
Answer 91409 by jim_thompson5910(28593) on 2008-02-03 21:48:51 (Show Source):
You can put this solution on YOUR website!
 Start with the given equation
 Multiply both sides by the LCM of 9. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)
 Distribute and multiply the LCM to each side
 Add 63 to both sides
 Combine like terms on the right side
--------------------------------------------------------------
Answer:
So our answer is
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Graphs/124700: Solve the system by substitution.
2x – 4y = 18
y = –x – 12
1 solutions
Answer 91407 by jim_thompson5910(28593) on 2008-02-03 21:38:44 (Show Source):
You can put this solution on YOUR website!Start with the given system
Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.
Distribute
Combine like terms on the left side
Subtract 48 from both sides
Combine like terms on the right side
Divide both sides by 6 to isolate x
Divide
Now that we know that , we can plug this into to find
Substitute for each
Simplify
So our answer is and which also looks like
Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer.
Graph of (red) and (green)
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Equations/124703: Write the equation of the line with slope –7 and y-intercept (0, 5).
1 solutions
Answer 91406 by jim_thompson5910(28593) on 2008-02-03 21:35:08 (Show Source):
You can put this solution on YOUR website!
If you want to find the equation of line with a given a slope of  which goes through the point (  ,  ), you can simply use the point-slope formula to find the equation:
---Point-Slope Formula---
where is the slope, and is the given point
So lets use the Point-Slope Formula to find the equation of the line
 Plug in  ,  , and  (these values are given)
 Distribute
 Multiply and  to get
 Add 5 to both sides to isolate y
 Combine like terms and to get
------------------------------------------------------------------------------------------------------------
Answer:
So the equation of the line with a slope of which goes through the point ( , ) is:
which is now in form where the slope is and the y-intercept is 
Notice if we graph the equation and plot the point ( , ), we get (note: if you need help with graphing, check out this solver)
 Graph of through the point (,)
and we can see that the point lies on the line. Since we know the equation has a slope of and goes through the point (,), this verifies our answer.
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Graphs/124692: The sum of two numbers is 29. Their difference is 7. What are the two numbers
1 solutions
Answer 91403 by jim_thompson5910(28593) on 2008-02-03 21:20:44 (Show Source):
You can put this solution on YOUR website!The sentence "The sum of two numbers is 29" translates to the equation 
The sentence "Their difference is 7" translates to the equation 
Start with the given system of equations:
Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.
So let's isolate y in the first equation
Start with the first equation
 Subtract from both sides
 Rearrange the equation
 Divide both sides by
 Break up the fraction
Reduce
---------------------
Since , we can now replace each in the second equation with  to solve for
 Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.
 Distribute the negative
 Combine like terms on the left side
 Add 29 to both sides
 Combine like terms on the right side
 Divide both sides by 2 to isolate x
 Divide
-----------------First Answer------------------------------
So the first part of our answer is:
Since we know that we can plug it into the equation (remember we previously solved for in the first equation).
Start with the equation where was previously isolated.
 Plug in
 Multiply
 Combine like terms
-----------------Second Answer------------------------------
So the second part of our answer is:
-----------------Summary------------------------------
So our answers are:
and
which form the point )
So the two numbers are 18 and 11
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Inequalities/124678: Find the solution set
1 solutions
Answer 91384 by jim_thompson5910(28593) on 2008-02-03 19:39:58 (Show Source):
You can put this solution on YOUR website! Start with the given inequality
 Multiply both sides by the LCD  . Doing this will eliminate every fraction.
 Distribute and multiply. Notice every denominator has been canceled out.
 Foil
 Distribute the negative
 Get every term to the left side
 Combine like terms
If we set  equal to zero and solve, we'll find that the critical values are  or
Now let's test a value that is less than -3
Let 
Start with the given inequality
 Plug in
 Simplify
Since this inequality is true, this means that any values less than will satisfy the inequality
-------------------------------------
Now let's test a value that is in between -3 and 1
Let
Start with the given inequality
 Plug in
 Simplify
Since this inequality is not true, this means that any values in between -3 and 1 will not satisfy the inequality.
-------------------------------------
Now let's test a value that is in greater than 1
Let 
Start with the given inequality
 Plug in
Simplify
Since this inequality is true, this means that any values greater than will satisfy the inequality
---------------------------------
Answer:
So any values that are either less than -3 or greater than 1 will satisfy the inequality
In other words,  or 
So the solution in interval notation is
) U )
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Inequalities/124677: Find the solution set
1 solutions
Answer 91382 by jim_thompson5910(28593) on 2008-02-03 19:37:08 (Show Source):
You can put this solution on YOUR website! Start with the given compound inequality
 Multiply all sides by the LCD 10. This will eliminate the fractions
 Distribute and multiply
 Distribute again
 Add 24 to all sides
 Divide every side by 12 to isolate x.
 Reduce.
So the solution in interval notation is: (  ,  ]
Now let's graph the solution set
Note: at  there is a open circle (which means this point is excluded) and at  there is a closed circle (which means this point is included)
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Travel_Word_Problems/124676: A girl walked from her home into town at the rate of 4 miles per hour. She returned by bus over the same route. The bus averaged 20 miles per hour, and the entire round trip took 1 hour and 40 minutes, including the 10 minute wait for the bus. How far did the girl walk?
1 solutions
Answer 91381 by jim_thompson5910(28593) on 2008-02-03 19:34:37 (Show Source):
You can put this solution on YOUR website!Let  =walking time and  =driving time
Now we're going to use the distance-rate-time equation 
Since the walking speed is 4 mph and the walking time is , this means  and 
 Plug in and
Also, since the driving speed is 20 mph and the driving time is , this means  and 
 Plug in and
Because the distance is the same both ways, this means that 
 Start with the given equation
 Divide both sides by 4 to isolate
If the entire trip took 1 hour and 40 minutes and there was a 10 minute wait, then the traveling portion took 1 hour and 30 minutes (which is 1.5 hours)
So the sum of these two times is 1.5. In other words, we have this first equation
 Plug in
 Combine like terms
 Divide both sides by 6 to isolate
So the driving time is 0.25 hours or 15 minutes
Now let's go back to the equation
Start with the given equation
 Plug in our answer
 Multiply
So the distance that she traveled is 5 miles
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Radicals/124675: Solve.
1 solutions
Answer 91380 by jim_thompson5910(28593) on 2008-02-03 19:33:13 (Show Source):
You can put this solution on YOUR website! Start with the given equation
 Square both sides
 Square the right side to remove the square root
 Foil the left side
 Multiply
 Foil
 Combine like terms
 Subtract 2x from both sides. Add 5 to both sides.
 Combine like terms
 Divide both sides by 2
 Square both sides
 Subtract 4 from both sides.
 Factor the left side
Now set each factor equal to zero:
or 
or  Now solve for x in each case
So our possible answers are:
or
Check:
Let's verify the first solution
Start with the given equation
 Plug in
 Combine like terms
 Simplify
 Add. Since the two sides of the equation are not equal, this means that is not a solution.
-----------------
Let's verify the second solution
Start with the given equation
 Plug in
 Combine like terms
 Take the square root
 Add. Since the two sides of the equation are equal, this verifies the solution
So the only solution is
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Inequalities/124674: Solve. Express your answer in interval notation and graph
1 solutions
Answer 91379 by jim_thompson5910(28593) on 2008-02-03 19:30:04 (Show Source):
You can put this solution on YOUR website! Start with the given inequality
 or  Break up the absolute value
Now let's solve the first inequality
Start with the given inequality
 Add 14 to both sides
 Subtract 2x from both sides
 Combine like terms on the left side
 Divide both sides by 3 to isolate x
--------------------------------------------------------------
Answer:
So our answer is  (which is approximately  in decimal form)
Now let's solve the second inequality
Start with the given inequality
 Add 14 to both sides
 Add 2x to both sides
 Combine like terms on the left side
 Divide both sides by 7 to isolate x
 Divide
--------------------------------------------------------------
Answer:
So our answer is
--------------------------------------------------------------
Answer:
So our two answers are
or
So in interval notation our answer is
(-  ,2] U [14/3 , )
So if we graph the solutions, we get
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Linear-systems/124657: The sum of two numbers is 38. Their difference is 10. What are the two numbers?
1 solutions
Answer 91377 by jim_thompson5910(28593) on 2008-02-03 19:16:56 (Show Source):
You can put this solution on YOUR website!The sentence "The sum of two numbers is 38" translates to the equation 
The sentence "Their difference is 10" translates to the equation 
Start with the given system of equations:
Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.
So let's isolate y in the first equation
Start with the first equation
 Subtract from both sides
 Rearrange the equation
 Divide both sides by
 Break up the fraction
Reduce
---------------------
Since , we can now replace each in the second equation with  to solve for
 Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.
 Distribute the negative
 Combine like terms on the left side
 Add 38 to both sides
 Combine like terms on the right side
 Divide both sides by 2 to isolate x
 Divide
-----------------First Answer------------------------------
So the first part of our answer is:
Since we know that we can plug it into the equation (remember we previously solved for in the first equation).
Start with the equation where was previously isolated.
 Plug in
 Multiply
 Combine like terms
-----------------Second Answer------------------------------
So the second part of our answer is:
-----------------Summary------------------------------
So our answers are:
and
which form the point )
So the two numbers are 24 and 14
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Radicals/124652: Solve.
1) m squared - 6m = 16
2) x squared + 5x = 3
1 solutions
Answer 91373 by jim_thompson5910(28593) on 2008-02-03 19:09:07 (Show Source):
You can put this solution on YOUR website!# 1
 Start with the given equation
 Subtract 16 from both sides.
 Factor the left side (note: if you need help with factoring, check out this solver)
Now set each factor equal to zero:
 or 
 or  Now solve for m in each case
So our answer is
or
Notice if we graph  (just replace m with x) we can see that the roots are  and  . So this visually verifies our answer.
# 2
 Start with the given equation
 Subtract 3 from both sides.
Let's use the quadratic formula to solve for x:
Starting with the general quadratic
the general solution using the quadratic equation is:
So lets solve  ( notice  , , and  )
 Plug in a=1, b=5, and c=-3
 Square 5 to get 25
 Multiply  to get 
 Combine like terms in the radicand (everything under the square root)
 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
 Multiply 2 and 1 to get 2
So now the expression breaks down into two parts
 or 
Now break up the fraction
 or 
So these expressions approximate to
 or 
So our solutions are:
or
Notice when we graph  , we get:
when we use the root finder feature on a calculator, we find that and .So this verifies our answer
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Linear-systems/124654: Solve the system by substitution.
x + 5y = 11
–3x – 2y = –7
1 solutions
Answer 91371 by jim_thompson5910(28593) on 2008-02-03 19:05:17 (Show Source):
You can put this solution on YOUR website!
Start with the given system of equations:
Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.
So let's isolate y in the first equation
 Start with the first equation
 Subtract from both sides
 Rearrange the equation
 Divide both sides by
 Break up the fraction
 Reduce
---------------------
Since , we can now replace each in the second equation with  to solve for
 Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.
 Distribute to
 Multiply
 Multiply both sides by the LCM of 5. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)
 Distribute and multiply the LCM to each side
 Combine like terms on the left side
 Add 22 to both sides
 Combine like terms on the right side
 Divide both sides by -13 to isolate x
Divide
-----------------First Answer------------------------------
So the first part of our answer is:
Since we know that we can plug it into the equation (remember we previously solved for in the first equation).
Start with the equation where was previously isolated.
 Plug in
 Multiply
 Combine like terms and reduce. (note: if you need help with fractions, check out this solver)
-----------------Second Answer------------------------------
So the second part of our answer is:
-----------------Summary------------------------------
So our answers are:
and
which form the point )
Now let's graph the two equations (if you need help with graphing, check out this solver)
From the graph, we can see that the two equations intersect at . This visually verifies our answer.
 graph of (red) and  (green) and the intersection of the lines (blue circle).
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Linear-systems/124655: Solve the system by addition.
4x – 5y = –19
x + 3y = 8
1 solutions
Answer 91370 by jim_thompson5910(28593) on 2008-02-03 19:04:12 (Show Source):
You can put this solution on YOUR website!
Start with the given system of equations:
Now in order to solve this system by using elimination/addition, we need to solve (or isolate) one variable. I'm going to solve for y.
In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for , we would have to eliminate (or vice versa).
So lets eliminate . In order to do that, we need to have both coefficients that are equal in magnitude but have opposite signs (for instance 2 and -2 are equal in magnitude but have opposite signs). This way they will add to zero. By adding to zero, they can be eliminated.
So to make the coefficients equal in magnitude but opposite in sign, we need to multiply both coefficients by some number to get them to an common number. So if we wanted to get and to some equal number, we could try to get them to the LCM.
Since the LCM of and is , we need to multiply both sides of the top equation by and multiply both sides of the bottom equation by like this:
 Multiply the top equation (both sides) by
 Multiply the bottom equation (both sides) by
Distribute and multiply
Now add the equations together. In order to add 2 equations, group like terms and combine them
Combine like terms and simplify
 Notice how the x terms cancel out
 Simplify
 Divide both sides by  to isolate y
 Reduce
Now plug this answer into the top equation to solve for x
Start with the first equation
 Plug in
 Add 15 to both sides
 Combine like terms on the right side
 Divide both sides by 4 to isolate x
 Divide
So our answer is
and
which also looks like )
Now let's graph the two equations (if you need help with graphing, check out this solver)
From the graph, we can see that the two equations intersect at . This visually verifies our answer.
 graph of (red) and  (green) and the intersection of the lines (blue circle).
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Radicals/124660: Solve.
x squared - 6x - 3 = 0
1 solutions
Answer 91367 by jim_thompson5910(28593) on 2008-02-03 19:01:10 (Show Source):
You can put this solution on YOUR website!Let's use the quadratic formula to solve for x:
Starting with the general quadratic
the general solution using the quadratic equation is:
So lets solve  ( notice ,  , and )
 Plug in a=1, b=-6, and c=-3
 Negate -6 to get 6
 Square -6 to get 36 (note: remember when you square -6, you must square the negative as well. This is because  .)
 Multiply to get
 Combine like terms in the radicand (everything under the square root)
 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
 Multiply 2 and 1 to get 2
So now the expression breaks down into two parts
 or 
Now break up the fraction
 or 
Simplify
 or 
So these expressions approximate to
 or 
So our solutions are:
or
Notice when we graph  , we get:
when we use the root finder feature on a calculator, we find that and .So this verifies our answer
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