Question

解关于x的方程组:{(a-1)x+2y=a+1(1) 2x+(a-1)y=4(2)

Answer 1

①×（a-1）得：（a-1)²x+2(a-1)y=(a+1)(a-1)③

②×2得：4x+2(a-1)y=8④

④-③得：4x-(a-1)²x=8-(a+1)(a-1)

[4-(a-1)²]x=8-(a²-1)

[4-(a²-2a+1)]x=8-a²+1

[4-a²+2a-1]x=9-a²

(3-a²+2a)x=9-a²

x=9-a²/3-a²+2a

x=9-a²/-a²+2a+3

x=-(a+3)(a-3)/-(a-3)(a+1)

x=a+3/a+1