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Question 992474: PLS HELP.ME ANSWER THIS PLS..
Simplify the following Linear Equation.
Using Elimination,Substition,Determinants and Graphical.
1) 2x+3y=18
4x+6y=12
2) 4x+y=6
-8x-2y=21
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! Using:
1) 
| Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition |
Lets start with the given system of linear equations
In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).
So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.
So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 2 and 4 to some equal number, we could try to get them to the LCM.
Since the LCM of 2 and 4 is 4, we need to multiply both sides of the top equation by 2 and multiply both sides of the bottom equation by -1 like this:
 Multiply the top equation (both sides) by 2
 Multiply the bottom equation (both sides) by -1
So after multiplying we get this:
Notice how 4 and -4 and 36 and -6 add to zero (ie   )
However 36 and -12 add to 24 (ie  );
So we're left with
which means no value of x or y value will satisfy the system of equations. So there are no solutions
So this system is inconsistent |
2) 
| Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition |
Lets start with the given system of linear equations
In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).
So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.
So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 4 and -8 to some equal number, we could try to get them to the LCM.
Since the LCM of 4 and -8 is -8, we need to multiply both sides of the top equation by -2 and multiply both sides of the bottom equation by -1 like this:
 Multiply the top equation (both sides) by -2
 Multiply the bottom equation (both sides) by -1
So after multiplying we get this:
Notice how -8 and 8 and -12 and 2 add to zero (ie   )
However -12 and -21 add to -33 (ie  );
So we're left with
which means no value of x or y value will satisfy the system of equations. So there are no solutions
So this system is inconsistent |
1)
| Solved by pluggable solver: SOLVE linear system by SUBSTITUTION |
Solve:
 We'll use substitution. After moving 3*y to the right, we get:
 , or  . Substitute that
into another equation:
 and simplify: So, we know that y=24=0. Since , x=-27.
Answer:  .
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2)
| Solved by pluggable solver: SOLVE linear system by SUBSTITUTION |
Solve:
 We'll use substitution. After moving 1*y to the right, we get:
 , or  . Substitute that
into another equation:
 and simplify: So, we know that y=-33=0. Since , x=9.75.
Answer:  .
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1)
 by systems of linear equations are of the form
 and  where  is the coefficient determinant given by  .
in your case  , , , , ,and 
then you have:
determinant => => =>
since determinant equal to zero, this system has no solution
2)
in this case  , , , , ,and 
then you have:
determinant => => =>
 =>
so, determinant equal to zero, this system has no solution
1)
| Solved by pluggable solver: Solve the System of Equations by Graphing |
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 are parallel and will never intersect. So there are no solutions and the system is inconsistent. |
2)
| Solved by pluggable solver: Solve the System of Equations by Graphing |
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
 Add  to 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 are parallel and will never intersect. So there are no solutions and the system is inconsistent. |
Answer by ikleyn(52835)  (Show Source):
You can put this solution on YOUR website! .
1)
 .
Divide the second equation by 2. You will get
 .
Now compare two equations in this system. They have the same left parts and different right parts.
Hence, the system is inconsistent. You need not to make long calculations. You can establish it in couple lines.
2) The same approach works for the second system, too.
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