SOLUTION: solve the system of linear equations using the elimination method. x-2y=12 4x+2y=8

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Question 698139: solve the system of linear equations using the elimination method.
x-2y=12
4x+2y=8

Found 2 solutions by unlockmath, Stitch:
Answer by unlockmath(1688) About Me  (Show Source):
You can put this solution on YOUR website!
Hello,
Let's add both of these:
x-2y=12
4x+2y=8
to get:
5x=20
Divide by 5:
x=4
Now we can solve for y:
y=-4
Make sense?
RJ
www.math-unlock.com

Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Given: X+-+2Y+=+12
& 4X+%2B+2Y+=+8
Set both equations equal to zero
X+-+2Y+-12+=+0
4X+%2B+2Y+-+8+=+0
Notice that both equations contain a 2Y.
You need to multiply on of the equations by -1 to make the signs of the 2Y match
I choose the first one.
-X+%2B+2Y+%2B+12+=+0
Since both equations equal zero, you can set the equations equal to each other.
-X+%2B+2Y+%2B+12+=+4X+%2B+2Y+-+8
Subtract 2Y from both sides
-X+%2B+12+=+4X+-+8
Add 8 to both sides
-X+%2B+20+=+4X
Add X to both sides
20+=+5X
Divide both sides by 5
highlight%284+=+X%29
Now plug 4 into one of the equations for X and solve for Y
X+-+2Y+=+12
4+-+2Y+=+12
Add 2Y to both sides
4+=+12+%2B+2Y
Subtract 12 from both sides
-8+=+2Y
Divide both sides by 2
highlight_green%28-4+=+Y%29