SOLUTION: This question is on the Addition Method rather than the Substitution Method. When using the Addition Method won't you only solve for 1 variable? Here is the problem below: Proble

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Question 6087: This question is on the Addition Method rather than the Substitution Method. When using the Addition Method won't you only solve for 1 variable? Here is the problem below:
Problem:
(Eq.1) 3a + 2b = 8
(Eq.2) 5a + 2b =2
-1(3a) + -1(2b) = -1(8)
-3a + -2b = -8
5a + 2b = 2
_______________
2a = -6
2a/2 = -6/2
a = -3
If I canceled out "b" how do I solve for "b".
My instructor wrote this on my test:
b=?
Thanks,
TSJ

Found 2 solutions by Abbey, guapa:
Answer by Abbey(339) (Show Source):
You can put this solution on YOUR website!
once you found a, you put it back into the equation to find b:
3(-3)+2b=8
-9+2b=8
2b=17
b=17/2
then verify with both numbers in the other equation:
5(-3)+2(17/2)=2
-15+17=2 - this is a true statement, so the solution is = (-3,17/2) - this is written in parentheses because the solution is actually where these two lines intersect on a graph - a single point.

Answer by guapa(62) (Show Source):
You can put this solution on YOUR website!
You always solve for both variables.
You did a great job by solving for a. In order to find b you just have to substitute a for -3 in any of the original equation. Just choose the one that is the easiest to solve for you.

Hope it helps