指數函數 解聯合方程

3^(x-2y) = 9^(x+1) .... (1)
5^(x-y) = 125 ... (2)

From (1), we have:
3^(x-2y) = 3^(2x+2)
x-2y = 2x+2
x = -2y-2 .... (3)

From (2), we have:
5^(x-y) = 5^3
x-y = 3 ... (4)

Sub. (3) into (4).
-2y-2-y = 3
-3y-2 = 3
y = -5/3

Sub. y = -5/3 into (3).
x = -2(-5/3) - 2
x = 4/3

3^(x-2y)=9^(x+1) i
5^(x-y)=125 ii
由i, 3^(x-2y)=3^(2)(x+1)
x-2y=2x+2
-2y=x+2
y=(x+2)/-2 iii
由ii, 5^(x-y)=5^3
x-y=3 iv
代iii入iv
x-(x+2)/2=3
2x-x+2=5
x=3
代x=3入iv
3-y=3
y=-1
所以
(x,y)=(3,-1)