解方程组lg(x-y)+lg(7x-8y)=2,2^(-x+3y)=4

来源:学生作业帮助网 编辑:六六作业网 时间:2024/07/12 01:49:09
解方程组lg(x-y)+lg(7x-8y)=2,2^(-x+3y)=4解方程组lg(x-y)+lg(7x-8y)=2,2^(-x+3y)=4解方程组lg(x-y)+lg(7x-8y)=2,2^(-x+

解方程组lg(x-y)+lg(7x-8y)=2,2^(-x+3y)=4
解方程组lg(x-y)+lg(7x-8y)=2,2^(-x+3y)=4

解方程组lg(x-y)+lg(7x-8y)=2,2^(-x+3y)=4
由 lg (x-y)+lg(7x-8y)=2,得
lg(x-y)(7x-8y)=2 (x-y)(7x-8y)=100 (1)
由 2^(-x+3y)=4,得
-x+3y=2
x=3y-2 (2)
把(2)代入(1)得
2(y-1)(13y-14)=100
13y²-27y-36=0
(13y+12)(y-3)=0
∴y1=-12/13 y2=3
x1=-36/13-2=-62/13 x2=7
即 ﹛x1=-62/13 ,y1=-12/13
﹛x2=7,y2=3