Question

2(x+y)+2(x-y)=3 ｛ 3(x+y)-2(x-y)=2 求解! 换元或整体方法

Answer 1

2(x+y)+2(x-y)=3
2x+2y+2x-2y=3
4x=3
x= 3/4
3(x+y)-2(x-y)=2
3x+3y-2x+2y=2
x+5y=2
5y=2-x = 2 - 3/4 = 5/4
y = 1/4
换元法：
令a=x+y b=x-y
则 2a+2b=3 ① 3a-2b=2 ②
①+②得 5a=5 a=1
代入①得 2+2b=3 b=1/2
∴ x+y=1 x-y=1/2
两式相加：2x = 3/2 x=3/4
两式相减：2y = 1/2 y = 1/4