Questions on Algebra: Systems of Linear Equations answered by real tutors!

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Question 241489: (x/4)-(y/3)=1
write in standard form
Answer by unlockmath(121)

(Show Source):

You can put this solution on YOUR website!
Hello,
Let's take the fractions away by multiplying everything by 12.
12(x/4)-12(y/3)=12 or 3x-4y=12 There we go, it's in general form now.
RJ Toftness
www.math-unlock.com

Question 241488: (5/x)-(2/y)=7
write in standard form
Answer by stanbon(26297)

(Show Source):

You can put this solution on YOUR website!
(5/x)-(2/y)=7
---
Multiply thru by xy to get:
5y - 2x = 7xy
===================
Cheers,
stan H.

Question 241396: 4x-5y=11
x+2y=7
Answer by checkley77(7072)

(Show Source):

You can put this solution on YOUR website!
4x-5y=11
-5y=-4x+11
y=-4x/-5+11/-5
y=4x/5-11/5 (red line)
x+2y=7
2y=-x+7
y=-x/2+7/2
y=-x/2+7/2 (green line)

(graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions 4x/5 -11/5 and -x/2 +7/2).
4x-5y=11
x+2y=7 multiply this equation by -4 & add
-4x-8y=-28
4x-5y=11
----------------
-13y=-17
y=-17/-13
y=17/13 or 1.3 ans.
x+2*17/13=7
x+34/13=7
x=7-34/13
x=4.38 ans.
Intercept (4.38,1.30)

Question 241438: Find the soultion to the system of equations.
4x + 1 over 2y = -12
3x + 2y = 4
Answer by checkley77(7072)

(Show Source):

You can put this solution on YOUR website!
4x + y/2 = -12 multiply this equation by -4 & add
3x + 2y = 4
-16x-2y=48
------------------
-13x=52
x=52/-13
x=-4 ans.
4*-4+y/2=-12
-16+y/2=-12
y/2=-12+16
y/2=4
y=2*4
y=8 ans.
Proof:
3*-4+2*8=4
-12+16=4
4=4

Question 241439: Find the soultion to the system of equations.
x + 7y = -2
3x + y = 34
Answer by checkley77(7072)

(Show Source):

You can put this solution on YOUR website!
x + 7y = -2 multiply this equation by -3 & add.
3x + y = 34
-3x-21y=6
-------------------
-20y=40
y=40/-20
y=-2 ans.
x-7*-2=-2
x-14=-2
x=14-2
x=12 ans.
Proof:
3*12-2=34
36-2=34
34=34

Question 241421: Solve the system of equations.
x + 5y = 2
-6x + 5y = -47
Answer by jim_thompson5910(13794)

(Show Source):

You can put this solution on YOUR website!

Start with the given system of equations:

Multiply the both sides of the second equation by -1.

Distribute and multiply.

So we have the new system of equations:

Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

Group like terms.

Combine like terms.

Simplify.

Divide both sides by

to isolate

Reduce.

------------------------------------------------------------------

Now go back to the first equation.

Plug in

Subtract

from both sides.

Combine like terms on the right side.

Divide both sides by

to isolate

Reduce.

So the solutions are

and

.

Which form the ordered pair

.

This means that the system is consistent and independent.

Notice when we graph the equations, we see that they intersect at

. So this visually verifies our answer.

Graph of

(red) and

(green)

Question 240390: This is a textbook problem: which values in the table is the relationship linear? Tell how you decided. Write the equation for each linear relationship.
__________________________________________________________
x 5 10 15 20 25 30
__________________________________________________________
y 20 30 40 50 50 50
??? I first began by attempting to create an equation that would equal such as y=3(x)+5; this would make sense for (5,20) but not for the others
??? then I considered beginning by using the equation of a straight line y=mx+b; but if I plug in Im still not sure if it would equal???
Answer by Alan3354(6097)

(Show Source):

You can put this solution on YOUR website!
y = 2x + 10 fits the 1st 4 points.
There is no linear function that fits all 6 points.
-------------
It can be specified:
y = 2x + 10, y<=50 a linear function and a limit

Question 241239: Write the slope-intercept form of the equation for the line.

Found 2 solutions by College Student, checkley77:
Answer by College Student(217)   (Show Source):
You can put this solution on YOUR website!
The equation for the slope-interceot form of a line is:

But we can first find the slope by using:

.
By looking at the graph, our points are (-3,-2) and (3,4); so:

.
Thus we now move to the Slope-Intercept form:

Answer by checkley77(7072)   (Show Source):
You can put this solution on YOUR website!
The slope=1
The y intercept=1
The equation is:
Y=X+1

Question 241093: what is the answer and explation of x=6y-4,x=-2y+28
Answer by unlockmath(121)   (Show Source):
You can put this solution on YOUR website!
Hello,
We can attack this problem from a couple different ways so let's take the easy route. Let's multiply the second equation by 3.(I'm doing this so the y cancels)Also note when you multiply everything needs to be multiplied.
(3)x=(3)-2y+(3)28 or 3x=-6y+84
x=6y-4
3x=-6y+84 Now we can add both equations together which will give us:
4x=80 Divide both sides by 4
x=20 Plug this answer into the original equation (either equation will work)
20=6y-4 Add 4 to both sides
24=6y Divide both sides by 6
4=y There we go plug these answers y=4 and x=20 into both equations and it should work out.
RJ Toftness
www.math-unlock.com

Question 241002: When you solve a system of equations by the addition method, how do you determine whether the system of equations is inconsistent?
Answer by stanbon(26297)   (Show Source):
You can put this solution on YOUR website!
When you solve a system of equations by the addition method, how do you determine whether the system of equations is inconsistent?
----------------------
It is inconsistent if one or more of the equations
is a contradiction, i.e. 0 = 2
=====================================
Cheers,
Stan H.

Question 240926: i need help on solving for elmination, i get confused.
Problem: 2x+6y=17
2x-10y=9
break it down for me step by step, if you can..thank you! :)
Answer by edjones(3299)   (Show Source):
You can put this solution on YOUR website!
2x+6y=17
2x-10y=9
----------------subtract
==>16y=8
y=1/2
.
2x+3=17 replace y with 1/2
2x=14
x=7
.
Ed

Question 240875: i solved this problem and i keep coming up with decimal answers, i am stuck please help....
"solving system of linear equation by elimination"
problem( x+y=-16)
3x+y=-30
Answer by Alan3354(6097)   (Show Source):
You can put this solution on YOUR website!
x+y=-16
3x+y=-30
----------- Subtract
-2x = 14
x = -7
---------
y = -9

Question 240791: How do you write an equation for a line that is parallel to a given line and passes through a given point
(1,3) y=-4x+5
Answer by vleith(1977)   (Show Source):
You can put this solution on YOUR website!
Look at this solver --> http://www.algebra.com/algebra/homework/Linear-equations/equation-parallel-or-perpendicular.solver

Question 240749: How do you Graph 5x+2y=4
Answer by solver91311(5072)   (Show Source):
You can put this solution on YOUR website!

Step 1. Pick a value for x. It can be anything you like, but 0, 1, or some other small integer usually works well and makes the arithmetic easier.

Step 2. Substitute that value in place of x in your equation. Do the arithmetic and determine the value of y that results.

Step 3. Take the value of x that you selected for step 1 and the value of y that you calculated in step 2 and form an ordered pair (x,y).

Step 4. Plot the ordered pair from Step 3 on your graph. Remember that the x value is the distance right or left along the horizontal axis and the y value is the distance up or down along the vertical axis.

Step 5. Repeat steps 1 through 4 with a different value for x.

Step 6. Draw a line across your graph that passes through the two points that you plotted.

John

Question 240641: It's me again, I don't know how to solve the system of equations by substitution. {5x-2y= -1
{x+4y= 35
last question then I will leave you alone until next term in school.
Solve the inequality. Give the solution in interval form.

3(5x-1)-2x>13=7
Thank-you so much for your time and patience.
Answer by rapaljer(3625)   (Show Source):
You can put this solution on YOUR website!
To solve by substitution method, you need to solve for one variable in terms of the other in one of the equations. In your problem, the easiest one to solve for is to solve for x in the second equation:

x=-4y +35

Now, substitute this into the first equation:
5x-2y=-1
5(______)-2y=-1
5(-4y+35)-2y=-1
-20y + 175-2y=-1
-22y+175=-1
-22y=-176
y=8

Now, substitute this value y=8 back into they x= equation:
x=-4y+35
x=-4(8)+35
x=-32+35
x=3

The solution is (3,8).

Check:
Substitute both values of x and y into the OTHER equation:
5x-2y=-1
5(3)-2(8)=-1
15-16=-1 , IT CHECKS!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

Question 240634: Solve.
(x+2)(x-11)(x+1)>0
The solution set is {x|___}
Answer by rapaljer(3625)   (Show Source):
You can put this solution on YOUR website!
Are you allowed to use a graphing calculator or graphing techniques???

If so, then sketch y=(x+2)(x-11)(x+1).

This graph has zeros at x=-2, x=11, and x=-1. Sketch the graph using x values (based upon the zeros that you just found!) from x=-5 to x = 15. Values of y must be larger, but you can try using values from -100 to 100. I'll use the algebra.com calculator and see what it looks like:

Now, since you are solving the inequality (x+2)(x-11)(x+1)>0, you need to find all values of x for which the graph y=(x+2)(x-11)(x+1) are ABOVE the x axis.

This would be values of x from -2 to -1 or values of x from 11 to infinity.
{x|-2 < x <-1} U {x|x > 11}

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida

Question 240611: How do you solve by elimination using multiplication:
-3x+4y=12
2x+y=-8
Answer by unlockmath(121)   (Show Source):
You can put this solution on YOUR website!
Hello,
Let's multiply the second equation by -4 which will give us:

-3x+4y=12
-8x-4y=32
Now we can add both equations to give us:
-11x=44
Now we can divide both sides by -11 to give us:
x=-4
Plug in -4 to the original equation to find y.
-3(-4)+4y=12
12+4y=12 Subtract 12 to both sides
4y=0
y=0 and x=-4
There you go. To see if these are correct plug the answers into both equation and it should come out good.
RJ Toftness
www.math-unlock.com

Question 240551: can you show me the correct formula for x+5y=13
-2x+4y=16
Answer by jim_thompson5910(13794)   (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:

Multiply the both sides of the first equation by 2.

Distribute and multiply.

So we have the new system of equations:

Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

Group like terms.

Combine like terms.

Simplify.

Divide both sides by to isolate .

Reduce.

------------------------------------------------------------------

Now go back to the first equation.

Plug in .

Multiply.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So the solutions are and .

Which form the ordered pair .

This means that the system is consistent and independent.

Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.

Graph of (red) and (green)

Question 240568: y=x+2
y=-x+4
How Do You Solve This System?

Answer by jim_thompson5910(13794)   (Show Source):
You can put this solution on YOUR website!
Hint: Since AND , this means that we can set the right sides equal to one another to get . Solve this equation for 'x' to find its value. Once you have 'x', you can plug it into either given equation to find 'y'.

Question 240476: Factor(a+4)^2-2(a+4)+1
Answer by jim_thompson5910(13794)   (Show Source):
You can put this solution on YOUR website!
Hint: if we let and apply the appropriate substitutions, we go from to . Now factor . Once you have factored out, plug back in.

Question 240184: I need to solve for x and y by using substitution. I am not sure of how to go about doing this problem. If someone could help I would appreciate it. The problem is:
{y=8-3x
{2x-5y=11
I know that I need to multiply one problem to make the y's cancel but I am not sure.
Thanks
Answer by ankor@dixie-net.com(6693)   (Show Source):
You can put this solution on YOUR website!
I need to solve for x and y by using substitution.
y = 8 - 3x
2x - 5y = 11
:
Note that y = (8-3x), substitute this for y in the 2nd equation
2x - 5(8-3x) = 11
Multiply what's inside the brackets, change the signs inside the brackets
2x - 40 + 15x = 11
2x + 15x = 11 + 40
17x = 51
x =
x = 3
:
Use the 1st equation to find y, substitute 3 for x
y = 8 - 3(3)
y = 8 - 9
y = -1
:
:
Check solutions by substitution in the 2nd equation
2x - 5y = 11
2(3) - 5(-1) = 11
6 + 5 = 11; confirms our solutions
;
:
you made the statement,"I know that I need to multiply one problem to make the y's cancel"
This is not so in the substitution method. You've got it mixed up with the elimination method.

Question 240075: ok i need help with graphing slope and y-intercept the equation is y=3-2x
Answer by rfer(2688)   (Show Source):
You can put this solution on YOUR website!
y=3-2x
same as
y=-2x+3
y=mx+b
m=slope
b=y int
y=-2x+3

Question 240096: a system of linear equations that has the point (4,-7) as it's solution???
Answer by solver91311(5072)   (Show Source):
You can put this solution on YOUR website!

Sorry, but there is no verb in your question. I can't understand what it is that you want to do.

John

Question 240071: Solve by graphing.
x=-y (can't figure out slope)
x+y=4
Can't figure out where the two points meet.
Answer by solver91311(5072)   (Show Source):
You can put this solution on YOUR website!

You really don't need to figure the slope, you just need to perform the following steps once for each of your equations.

Step 1: Select a value for . It can be anything you want, but I suggest selecting a small integer.

Step 2: Substitute the selected value for in the equation, and then do the arithmetic to solve the equation for

Step 3: Create an ordered pair using the value of you selected in Step 1 and the value of you calculated in Step 2.

Step 4: Plot the ordered pair from Step 3 on your coordinate plane.

Step 5: Repeat Steps 1 through 4 once more using a different value for .

Step 6: Draw a line through the two plotted points.

Once you have graphed both lines, see where they intersect. That is, if they intersect. If you end up with two separate lines that do not intersect, then your solution set is the empty set. If you end up with two lines that do intersect in one point, your solution set is the ordered pair representing that point of intersection. If you end up with one line right on top of the other, then your solution set is the set of ordered pairs that satisfies either of the two equations. Such a set has in infinite number of elements.

On the other hand, if you do feel the need to determine the slope, then solve each of the equations for . That means do whatever is necessary (and follows the rules of algebra) to get all by itself on the left-hand side of the equal sign and everything else on the right-hand side.

For your first one:

Rewrite it:

Multiply by -1:

Once a two variable linear equation is solved for , then the equation is in slope-intercept form. That means that the slope is the coefficient on the term. The coefficient on your term is -1. Hence the slope is -1.

Do your other one the same way.

By the way: Congratulations. This is my 5000th answer on this site. You don't win anything and neither do I, but I just wanted to share.

John

Question 240004: please help me solve this equation
n(n-3)<54
a)9 b)3 c)10
Answer by checkley77(7072)   (Show Source):
You can put this solution on YOUR website!
n(n-3)<54
N^2-3N<54
N^2-3N-54<0
(N-9)(N+6)<0
N-9=0
N=9 ANS
N+6=0
N=-6 ANS.

Question 239785: Can you solve for x and y 8y=7+3x
Answer by checkley77(7072)   (Show Source):
You can put this solution on YOUR website!
8y=7+3x
y=7/8+3x/8 ans. for y.
3x=8y-7
x=8y/3-7/3 ans. for x.

Question 239817: solve by addition
x-2y=-1
-x+5y=4

Answer by checkley77(7072)   (Show Source):
You can put this solution on YOUR website!
x-2y=-1
-x+5y=4
-----------------
3Y=3
Y=3/3
Y=1 ANS.
X-2*1=-1
X-2=-1
X=-1+2
X=1 ANS.
PROOF:
-1+5=4
4=4

Question 239642: Hi I need help with a math problem. The question asks: Use the graph to write the equation of the line in slope-intercept form. Then write that equation in standard form. the x and y intercept are both -2 and the slope is -1. Thanks
Answer by Alan3354(6097)   (Show Source):
You can put this solution on YOUR website!
Use the graph to write the equation of the line in slope-intercept form. Then write that equation in standard form. the x and y intercept are both -2 and the slope is -1.
-----------
Use y = mx + b since the slope and y-intercept are given.
y = -x -2 slope-intercept form
x + y = -2 standard form

Question 239634: my son just cant understand algebra so is there aq book or something that could show him step by step to solve a problem
Answer by Alan3354(6097)   (Show Source):
You can put this solution on YOUR website!
There are a lot of books. Google algebra, there's a lot of stuff online.

Question 239549: The cost of producing 4 units is $204.80. The cost of producing 8 units is $209.60. How much does it cost to produce 12 units?
Answer by checkley77(7072)   (Show Source):
You can put this solution on YOUR website!
4x+y=204.80
-(8x+y=209.60) subtract
---------------------
-4x=-4.8
x=-4.8/-4
x=1.2 multiplier for each unit produced.
4*1.2+y=204.80
4.8+y=204.80
y=204.80-4.8
y=200 operating/overhead cost.
Proof:
8*1.2+200=209.60
9.6+200=209.60
209.60=209.60
12*1.2+200=14.4+200=$214.10 cost to produce 12 units.

Question 239526: Solve for X, Y, and Z in the following systems of three equations using either substition or elimination methods:
a. X + 2Y + Z = 6
X + Y = 4
3X + Y + Z = 8
b. 10X + Y + Z = 12
8X + 2Y +Z = 11
20X - 10Y - 2Z = 8
c. 22X + 5Y + 7Z = 12
10X + 3Y + 2Z = 5
9X + 2Y + 12Z = 14

Answer by Alan3354(6097)   (Show Source):
You can put this solution on YOUR website!
Solve for X, Y, and Z in the following systems of three equations using either substition or elimination methods:
X + 2Y + Z = 6
X + Y = 4
3X + Y + Z = 8
--------------
Eliminate one variable in 2 of the eqns by getting the same coefficients and eliminating.
Eliminate x
-----------
X + 2Y + Z = 6
X + Y = 4
--------------- Subtract
0x + y + z = 2 Eqn A
-----------------
X + Y = 4 times 3 --> 3x + 3y = 12
3X + Y + Z = 8
3x + 3y + 0z=12
----------------- Subtract
0x - 2y + z = -4 Eqn B
0x + y + z = 2 Eqn A
--------------- Subtract
-3y = -6
y = 2
------
z = 0
------
x = 2
=====================
Do the others the same way. email me for help, or to check your work @
gsihoutx@aol.com

Question 239550: There are 174 words typed in 3 minutes. There were 348 words typed in 6 minutes. How many words will be typed in 8 minutes?
Answer by checkley77(7072)   (Show Source):
You can put this solution on YOUR website!
174/3=58 words per minute.
348/6=58 ditto
8*58=464 words can be typed in 8 minutes.

Question 239421: One conveyor belt can move 1000 boxes in 12 minutes. Another can move 1000 boxes in 10 minutes. If another conveyor belt is added and all three are used, the boxes are moved in 3 minutes. How long would it take the third conveyor belt alone to do the same job?
Answer by ankor@dixie-net.com(6693)   (Show Source):
You can put this solution on YOUR website!
One conveyor belt can move 1000 boxes in 12 minutes.
Another can move 1000 boxes in 10 minutes.
If another conveyor belt is added and all three are used, the boxes are moved in 3 minutes.
How long would it take the third conveyor belt alone to do the same job?
:
Let x = time required by the 3rd conveyor to move 1000 boxes
:
Let the completed job = 1; (moving 1000 boxes)
:
A shared work equation:
+ + = 1
Multiply equation by 60x to eliminate the denominators, results:
5x(3) + 6x(3) + 60(3) = 60x
:
15x + 18x + 180 = 60x
:
33x + 180 = 60x
:
180 = 60x - 33x
:
180 = 27x
x =
x = 6 min
:
:
Check on a calc: enter (3/12) + (3/10) + (3/6.67) ~ 1

Question 239420: What is five divided by the sum of a number and 3, minus the quotient of 3 and the difference of the number and 3 is equal to 6 times the reciprocal of the difference of the number squared and 9. What is the number?
Found 2 solutions by Edwin McCravy, JimboP1977:
Answer by Edwin McCravy(2922)   (Show Source):
You can put this solution on YOUR website!
Tell Jimbo to bug off!
What is
five divided by the sum of a number and 3, minus the quotient of 3 and the difference of the number and 3 is equal to 6 times the reciprocal of the difference of the number squared and 9.

Replace "a number" and "the number" by x

five divided by the sum of x and 3, minus the quotient of 3 and the difference of x and 3 is equal to 6 times the reciprocal of the difference of x squared and 9.

five divided by the sum of x and 3, minus the quotient of 3 and the difference of x and 3 is equal to 6 times the reciprocal of the difference of x squared and 9.

Replace "the sum of x and 3" by "x+3"

five divided by x+3, minus the quotient of 3 and the difference of x and 3 is equal to 6 times the reciprocal of the difference of x squared and 9.

five divided by x+3, minus the quotient of 3 and the difference of x and 3 is equal to 6 times the reciprocal of the difference of x squared and 9.

Replace "the difference of x and 3" by "x-3":

five divided by x+3, minus the quotient of 3 and x-3 is equal to 6 times the reciprocal of the difference of x squared and 9.
five divided by x+3, minus the quotient of 3 and x-3 is equal to 6 times the reciprocal of the difference of x squared and 9.

Replace "five divided by x+3" by :

minus the quotient of 3 and x-3 is equal to 6 times the reciprocal of the difference of x squared and 9.
minus the quotient of 3 and x-3 is equal to 6 times the reciprocal of the difference of x squared and 9.

Replace "the quotient of 3 and x-3" by

minus is equal to 6 times the reciprocal of the difference of x squared and 9.
minus is equal to 6 times the reciprocal of the difference of x squared and 9.

Replace "x squared" by

minus is equal to 6 times the reciprocal of the difference of and 9.
minus is equal to 6 times the reciprocal of the difference of and 9.

Replace "the difference of and 9" by

minus is equal to 6 times the reciprocal of .
minus is equal to 6 times the reciprocal of .

Replace "the reciprocal of " by

minus is equal to 6 times .
minus is equal to 6 times .

Replace by

is equal to 6 times .
is equal to 6 times .

Replace "6 times by . is equal to . is equal to .
Replace "is equal to" by " = ":

Can you solve that? If not post again asking how. Answer = 15 Edwin

Answer by JimboP1977(76)   (Show Source):
You can put this solution on YOUR website!
I retract what I said and bow to Edwin's superior intellect and knowledge. Grateful though if you could remove your comment directed towards me.

Question 239149: can you show me how to do this: dirct variation equations
X 1 2 3 4 6
Y 5 10 15 20 30
For the formula of y=ax

Answer by checkley77(7072)   (Show Source):
You can put this solution on YOUR website!
y=ax
1=a*5
a=1/5 answer.
Proof:
y=x/5
1=5/5
1=1
y=x/5
6=30/5
6=6

Question 239095: solve by elimination method: 3x - 9y = 2 and 3x - 9y = 3
Found 2 solutions by Alan3354, checkley77:
Answer by Alan3354(6097)   (Show Source):
You can put this solution on YOUR website!
There is no solution, unique or otherwise.

Answer by checkley77(7072)   (Show Source):
You can put this solution on YOUR website!
3x - 9y = 2
-(3x - 9y = 3) SUBTRACT THESE EQUATIONS.
--------------------
0X+0Y=-1
0=1 THERE IS NO UNIQUE SOLUTION FOR X & Y.

Question 239045: Okay, i kinda asked a question like this earlier but i forgot one thing.
A chart shows ideal heights and weights for adults with a medium build. A person with the height of 6o inches should have a weight of 112 pounds and a person with the height of 66 inches should have a weight of 136.
Write a linear equation to estimate the weight of a person of any height.
HOW DO I DO THAT?

Answer by Theo(675)   (Show Source):
You can put this solution on YOUR website!
60 inches = 112 pounds
66 inches = 136 pounds

let x = inches and y = pounds

(x1,y1) = 60,112)
(x2,y2) = 66,136)

slope of straight line = y2-y1/(x2-x1) = (136-112)/(66-60) = 24/6 = 4

slope-intercept form of straight line equation is y = mx+b where m is the slope and b is the y-intercept.

your equation is y = 4x + b because it has a slope of 4.

substitute either one of the points (x1,y1) or (x2,y2) in the equation to solve for the y-intercept which is b.

equation of y = 4x + b becomes:

112 = 4*60 + b if we use (x1,y1).

solving for b we get:

112 = 240 + b
b = 112-240 = -128

equation becomes y = 4x - 128

graph of this equation looks like:

the graph has y = 112 and 136 to show you that they occur at x = 60 and x = 66 as they should.

lso not very accurate although not quite as bad as on the low end.

If you restricted the domain for the value of x being from 50 to 70 then the graph straight line project might be ok.

Since this graph is a straight line calculated between only 2 points, it doesn't accurately portray the height to weight ratio at the extremes of the height range.

Question 238242: x=3y
Answer by College Student(217)   (Show Source):
You can put this solution on YOUR website!
Hello. The only thing I can tell you is to plug in a numeric value for one of the variables to find what the other variable would be. Other than that, you would need to resubmit the problem with full instructions as to what you need to do with the equation. Thank you! :)

Question 238838: Solve for X and Y in the following problems using either substitution or elimination methods. Make sure you show all your work so you can get partial credit even if your final answer is wrong.
a. X + Y= 6 , 2X + Y = 8
b. 7X + 3Y = 14 , 5X + 9Y = 10
c. 4X + Y = 16 , 2X + 3Y = 24
d. 12X + Y = 25 , 8X - 2Y = 14

Answer by checkley77(7072)   (Show Source):
You can put this solution on YOUR website!
a.
X + Y = 6
-(2X + Y = 8) SUBTRACT.
------------
-X=-2
X=2 ANS.
-2+Y=6
Y=6+2
Y=8 ANS.
2*2+Y=8
4+Y=8
Y=8-4
Y=4 ANS.
PROOF:
2+4=6
6=6
2*2+4-8
4+4=8
8=8
b.
7X + 3Y = 14 MULTIPLY BUY -3 & ADD
5X + 9Y = 10
-21X-9Y=-42
------------------
-16X=-32
X=-32/-16
X=2 ANS.
7*2+3Y=14
14+3Y=14
3Y=14-14
3Y=0
Y=0 ANS.
PROOF:
5*2+9*0=10
10=10
c.
4X + Y = 16 MULTIPLY BY -3 & ADD
2X + 3Y = 24
-12X-3Y=-48
-----------------
-10X=-24
X=-24/-10
X=2.4 ANS.
4*2.4+Y=16
9.6+Y=16
Y=16-9.6
Y=6.4 ANS.
PROOF:
2*2.4+3*6.4=24
4.8+19.2=24
24=24
d.
12X + Y = 25 MULTIPLY BY 2 & ADD .
8X - 2Y = 14
24X+2Y=50
---------------
32X=64
X=64/32
X=2 ANS.
12*2+Y=25
24+Y=25
Y=25-14
Y=1 ANS.
PROOF:
8*2-2*1=14
16-2=14
14=14

Question 238703: can someone please show me how to solve this step by step? I need to simplify this.
7{[4(a-4)+16] - [2(3a-2)+2]}
Answer by ankor@dixie-net.com(6693)   (Show Source):
You can put this solution on YOUR website!
simplify this.
7{[4(a-4)+16] - [2(3a-2)+2]}
:
start with the inmost brackets first, multiply what's in those brackets
7{[4a -16 + 16] - [6a - 4 + 2]}
:
Do the math inside the brackets
7(4a - (6a - 2))
:
Remove the inner bracket, a minus changes the signs
7(4a - 6a + 2)
:
combine the a's
7(-2a + 2)
then mult each term by 7
-14a + 14

Question 238626: Solve the system by the elimination method.
5x + 5y = -13
7x - 3y = 19
I'm having a hard time understading this equation.
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(6097)   (Show Source):
You can put this solution on YOUR website!
Solve the system by the elimination method.
5x + 5y = -13
7x - 3y = 19
-------------
To eliminate one of the variables, multiply one or both eqns to get the same coefficient for one of them. You can do either, I'll do y
--------
5x + 5y = -13 x3 --> 15x + 15y = -39
7x - 3y = 19 x5 --> 35x - 15y = 95
--------------------------------------
15x + 15y = -39
35x - 15y = 95
--------------- Add
50x = 56
x = 56/50 = 1.12
-----------------
Usually it's "elimination and substution", once you find one, you can sub and find the others.
7x - 3y = 19
7*1.12 - 3y = 19
3y = 7.84 - 19 = - 11.16
y = -3.72

Answer by stanbon(26297)   (Show Source):
You can put this solution on YOUR website!
Solve the system by the elimination method.
5x + 5y = -13
7x - 3y = 19
--------------------------
Multiply thru the 1st Eq by 3
Multiply thru the 2nd Eq by 5
--------------------------
15x + 15y = -39
35x - 15y = 95
------------
Add and solve for "x":
50x = 46
x = 23/25
-------------------
Substitute into 5x + 4y = -13
5(23/25) + 4y = -13
(23/5) + 4y = (-65/5)
4y = -88/5
y = -22/5
=====================
Cheers,
Stan H.