SOLUTION: solve each system by the elimination method 1)3x+2y=10 2x+y=7 2)3x-2y=7 2x-y=8 3)2x+3y=-13 -4x+6y=-10

Algebra ->  Linear-equations -> SOLUTION: solve each system by the elimination method 1)3x+2y=10 2x+y=7 2)3x-2y=7 2x-y=8 3)2x+3y=-13 -4x+6y=-10      Log On


   

Question 167382: solve each system by the elimination method
1)3x+2y=10
2x+y=7
2)3x-2y=7
2x-y=8
3)2x+3y=-13
-4x+6y=-10
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
1)3x%2B2y=10, EQN 1
2x%2By=7, EQN 2
Multiply EQN 2 by -2: --> -4x-2y=-14, then add to EQN 1
-x=-4 -->highlight%28x=4%29--system%283x%2B2y=10%2C-4x-2y=-14%29
Via EQN 1: 3%284%29%2B2y=10
12%2B2y=10 ---> 2y=10-12=-2 ---> cross%282%29y%2Fcross%282%29=cross%28-2%291%2Fcross%282%291+
highlight%28y=-1%29
Check Via EQN 2:
2%2A4%2B%28-1%29=7
8-1=7, good
2)3x-2y=7, EQN 3
2x-y=8 , EQN 4
Multiply EQN 4 by -2---> -4x%2B2y=-16 then add to EQN 3
-x=-9 --> highlight%28x=9%29 --system%283x-2y=7%2C-4x%2B2y=-16%29
Via EQN 3: 3%2A9-2y=7
27-7=2y ---> cross%2820%2910%2Fcross%282%29=cross%282%29y%2Fcross%282%29
highlight%28y=10%29
Check Via EQN 4:
4%2A9-2%2A10=16
36-20=16, good
3)2x%2B3y=-13, EQN 5
-4x%2B6y=-10, EQN 6
Multiply EQN 5 by -2 ----> -4x-6y=26 then add to EQN 6
-8x=16 --> x=16%2F-8=highlight%28-2=x%29 ---system%28-4x-6y=26%2C-4x%2B6y=-10%29
Via EQN 5: %282%29%28-2%29%2B3y=-13
3y=-13%2B4=-9 ---> cross%283%29y%2Fcross%283%29=cross%28-9%293%2Fcross%283%29
highlight%28y=-3%29
Check Via EQN 6:
%28-4%29%28-2%29%2B%286%29%28-3%29=-10
8%2B%28-18%29=-10
-10=-10 good
Thank you,
Jojo

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