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

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
RELATED QUESTIONS
6x+3y=0 8x+5y=8 using either the substitution method or the addition method (answered by mxgirl22)
Could you please help me solve this? Solve using the addition method or the substitution... (answered by solver91311)
This is the last one I had trouble with, again thank you all! Using substitution or... (answered by venugopalramana)
Solve the system using the substitution method or the elimination-by-addition method. 2x (answered by solver91311)
solve each system using the substitution method or the addition method 3(2x+y)=4x+20... (answered by mananth)
how do you solve this equation: 4x-8=4y, 4y+8=4x using the addition... (answered by Alan3354,MathLover1)
2x+y=0 x-2y=-10 Solve using the addition or substitution... (answered by stanbon)
How do you solve x-2y=5 2x-y=16 using either the substitution or addition method (answered by josmiceli)