SOLUTION: Hi, my name is Will and I am having a hard time solving systems of linear equations particularly this problem: 3x+2y=2 -2x+y=8

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Question 641351: Hi, my name is Will and I am having a hard time solving systems of linear equations particularly this problem:
3x+2y=2
-2x+y=8
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

you have a system to solve:
3x%2B2y=2......1
-2x%2By=8.......2
______________________________

3x%2B2y=2......1...first solve this one for y
2y=2-3x...both sides divide by 2
2y%2F2=2%2F2-3x%2F2
y=1-%283%2F2%29x..........now plug in equation 2 and solve for x
_________________
-2x%2B%281-%283%2F2%29x%29=8.......2
-2x%2B1-%283%2F2%29x=8both sides multiply by 2
-2x%2A2%2B1%2A2-%283%2F2%29%2A2x=8%2A2
-4x%2B2-3x=16
-7x%2B2=16
-16%2B2=7x
-14=7x
-14%2F7=x
highlight%28-2=x%29....now, plug it in y=1-%283%2F2%29x and solve for y
________________
y=1-%283%2F2%29%28-2%29
y=1-%283%2Fcross%282%29%29%28-cross%282%29%29..you will have.-3%2F-1=3
y=1%2B3
highlight%28y=4%29

check: plug in x=-2 and y=4
3x%2B2y=2......1
3%28-2%29%2B2%2A4=2
-6%2B8=2
2=2

-2x%2By=8.......2
-2%28-2%29%2B4=8
4%2B4=8
8=8

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Hi, my name is Will and I am having a hard time solving systems of linear equations particularly this problem:
3x+2y=2
-2x+y=8

system%283x+%2B+2y+=+2_____eq%28i%29%2C+-+2x+%2B+y+=+8+____+eq_%28ii%29%29

If you choose to solve it by substitution, then solve for y in eq (ii), and then substitute that value in eq (i). This will give you the value of x. Substitute the x-value in any of the 2 equations to obtain your y-value.

If you choose to use elimination, then just multiply eq (ii) by - 2, and add this new equation to eq (i). This will give you the value of x. Substitute the x-value in any of the 2 equations to obtain your y-value.

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