Question 970337
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