2x+3y=7(1)
3x-y=8(2)
(2)*3得：9x-3y=24(3)
(1)+(3)得：11x=31.x=31/11
将x=31/11带入（2）得：y=5/11
将x=31/11,y=5/11带入ax+by=1,2ax-3by=7得方程组
31/11*a+5/11*b=1(4)
62/11*a-15/11*b=7(5)
(4)*2得：62/11a+10/11b=2(6)
(6)-(5)得：25/11b=-5,b=-11/5
将b=-11/5带入（4）得：a=22/31
所以a=22/31,b=-11/5