Question

三个同学对问题“若方程组 a1x+b1y=c1,的解是 x=1,求方程组 a2x+b2y=c2 y=2.

Answer 1

根据题意可知

a1+2b1=c1 a2+2b2=c2
将c1和c2带入方程2
a1x+2b1y=3(a1+2b1)......... 1)
a1(x-3)=2b1(3-y) ............ 1_1)
a1x+2b2y=3(a2+2b2) 2)
a2(x-3)=2b2(3-y) .......... 2_1)
综合1_1)和2_1) 可知x=3 y=3 时可以成立
若1_1)和2_1)都不等于0
则a1/a2=b1/b2

Answer 2

a1x+2b1y=3c1 (a1x+2b1y)/3=c1 a1(x/3)+b1(2y/3)=c1 a2x+2b2y=3c2 (a2x+2b2y)/3=c2 a2(x/3)+b2(y/3)=c2 x/3=1 x=3 y/3=2 y=6方程组 a1x+2b1y=3c1 a2x+2b2y=3c2 的解为 x=3 y=6