解方程组2(x-y)/3-x+y/4=-1 6(x+y)-4(x-y)=12 怎样能简便一点解

题目

解方程组2(x-y)/3-x+y/4=-1 6(x+y)-4(x-y)=12 怎样能简便一点解

答案

解方程组2(x-y)/3-(x+y)/4=-1,6(x+y)-4(x-y)=12,怎样能简便一点解
2(x-y)/3-(x+y)/4=-1.(1)
6(x+y)-4(x-y)=12.(2)
由(2)得2(x-y)-3(x+y)=-6.(3)
由(1)得8(x-y)-3(x+y)=-12.(4)
(4)-(3)得6(x-y)=-6,故x-y=-1.(5)
将(5)代入(3)式得3(x+y)=-2+6=4,故x+y=4/3.(6)
(5)+(6)得2x=1/3,故x=1/6；代入(6)得y=4/3-x=4/3-1/6=7/6.