SOLUTION: If (2, -1) is a solution to the system of equations, what is the value of b? 2x+y=a 3x-y=b

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Question 970337: If (2, -1) is a solution to the system of equations, what is the value of b?
2x+y=a
3x-y=b
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
2x+y=a
3x-y=b
Add them
5x=a+b
;; 10=a+b
Now multiply top by 3 and bottom by -2
6x+3y=3a
-6x+2y=-2b
5y=3a-2b
;; -5=3a-2b
a+b=10
3a-2b=-5
2a+2b=20 ; doubling the first. Now add
3a-2b=-5
5a=15 ; a=3
a=3, b=7 ANSWER
2x+y=3
3x-y=7
5x=10 x=2 2x+y=3, 4+y=3 ; y=-1 solutions (2,-1) as they should be