Question

解方程组： {（x+2)^2-(y-3)^2=(x+y)(x-y) { x-3y=2

Answer 1

(x+2)^2-(y-3)^2=(x+y)(x-y) ......(1)
x-3y=2 ...... (2)
由（1）得：
x²+4x+4-y²+6y-9=x²-y²
4x+6y=5 ....(3)
(2)*2+(3)：
2x+4x = 4+5
6x=9
x=3/2
代入（2）得：
3/2-3y=2
3-6y=4
66=-1
y=-1/6

Answer 2

（x+2)^2-(y-3)^2=(x+y)(x-y)
x²+4x+4-y²+6y-9=x²-y²
4x+6y=5 (1)
x-3y=2 (2)
(1)+(2)*2 6x=9 x=3/2
代入(2) 3y=3/2-2 y=-1/6

Answer 3

{（x+2)^2-(y-3)^2=(x+y)(x-y)
展开得
x^2+4x+4-y^2+6y-9=x^2-y^2
即4x+6y-5=0
与 x-3y=2联立方程组得
x=3/2
y=-1/2

Answer 4

x=3/2
y=-1/6