SOLUTION: What is the solution to the system of equations: 2x +5y + 2z = 6 5x - 7y = -29 z = 1 I have tried this: SUBSTITUTION 2x + 5y + 2(1) = 6 2x + 5y = 4 I have tried to so

Question 107211: What is the solution to the system of equations:
2x +5y + 2z = 6
5x - 7y = -29
z = 1
I have tried this:
SUBSTITUTION
2x + 5y + 2(1) = 6
2x + 5y = 4
I have tried to solve for y using these equations:
2x + 5y = 4
5x - 7y = -29
MULTIPLY BY 2.5
5x + 7.5y = 10
I have tried to solve for y using these equations:
5x + 7.5y = 10
5x - 7y = -29
ELIMINATION
14.5y = 39
This would show that y > 2, but upon checking the answers from a resource (This is not a section of the textbook I am using), the answer is in fact, 2. Would you help me see where I made a mistake?

Found 2 solutions by Annabelle1, Earlsdon:
Answer by Annabelle1(69) (Show Source): You can put this solution on YOUR website!
you made a mistake when multiplying by 2.5
2.5*5 is 12.5 not 7.5
hope this helps
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Your error occured when you multiplied the equation by 2.5.
You have:
2.5(2x+5y = 4) = 5x+7.5y = 10 but 2.5(5y) = 12.5y, so the result should have been:
5x+12.5y = 10 now when you subtract the other equation:
5x-7y = -29 you get:
19.5y = 39 Dividing both sides by 19.5 gives you:
y = 2

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