Question

Solve: 6/x-1- 3/y-2=1, 5/x-1+1/y-2=2, where x is not 1 and y is not 2

Answer 1

$\text\bf{Given:}$

$\frac{6}{x-1}-\frac{3}{y-2}=1$

$\frac{5}{x-1}+\frac{1}{y-2}=2$

$\text{Take } u=\frac{1}{x-1}\;\&\; v=\frac{1}{y-2}$

$\text{We get ,}$

$6u-3v=1...........(1)$

$5u+v=2.............(2)$

$\textbf{solving (1) &(2)}$

$6u-3v=1...........(1)$

$15+3v=6$

$21u=7$

$\implies\;u=\frac{7}{21}$

$\implies\;u=\frac{1}{3}$

$\text{put }u=\frac{1}{3}\text{ in (1) }we get}$

$6(\frac{1}{3})-3v=1$

$\implies\2-3v=1$

$\implies 3v=1$

$\implies\;v=\frac{1}{3}$

$\text{when }u=\frac{1}{3},$

$\frac{1}{3}=\frac{1}{x-1}$

$\implies\;x-1=3$

$\implies\bf\;x=4$

$\text{when }v=\frac{1}{3},$

$\frac{1}{3}=\frac{1}{y-2}$

$\implies\;y-2=3$

$\bf\;y=5$

$\therefore\textbf{The solution is x=4 and y=5}$

Answer 2

Answer: https://brainly.app.link/qpzV02MawO​

Step-by-step explanation: