SOLUTION: My book isn't explaining this very well. Can you help? I'm to solve each system by elimination. 2(a+b)=94 4(a-9)=3b-23

Question 166092: My book isn't explaining this very well. Can you help?
I'm to solve each system by elimination.
2(a+b)=94
4(a-9)=3b-23
Found 2 solutions by checkley77, Mathtut:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
2(a+b)=94
2a+2b=94 multiply by -2 & add to the other equation
4(a-9)=3b-23
4a-36=3b-23
4a-3b=-23+36
4a-3b=13
-4a-4b=-188
------------------------
-7b=-188+13
-7b=-175
b=-175/-7
b=25 answer.
2(a+25)=94
2a+50=94
2a=94-50
2a=44
a=44/2
a=22 answer.
Proof:
4(22-9)=3*25-23
4*13=75-23
52=52

Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
2(a+b)=94
distribute
4(a-9)=3b-23
distribute

now we have 2a+2b=94
::: 4a-3b=13
when you use elimination method in linear equations you multiply one or both equations by a constant that will help eliminate one variable. I n our case we can either multiply the top equation by 4 and the bottom by -2 to eliminate the a variable or we can multiply the top by 3 and the bottom equation by 2 and get rid of the b variable. I choose the 2nd option
: 3(2a+2b=94)--->6a+6b=282
: 2(4a-3b=13)--->8a-6b= 26
now notice when we add
these two together that
the b terms are eliminated
and we end up with ------- 14a=308--->
now we can plug a's value back into either of the original equations solving for b
----------> 2(22)+2b=94----->44+2b=94--->2b=50---
hope that helps explain solving linear equations by elimination

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