Question

Solve for $x$ and $y$:
$\frac{6}{x-1}-\frac{3}{y-2}=1$
$\frac{5}{x-1}+\frac{1}{y-2}=2$, where $x\ne 1,y\ne 2$.

Answer 1

$\frac{6}{x-1}-\frac{3}{y-1}=1$ …………$\left(1\right)$

$\frac{5}{x-1}+\frac{1}{y-2}=2$ ……..$\left(2\right)$ $[$Here $x\ne 1,y\ne 2]$.

Multiply $\left(2\right)\times 3$.

$\left(2\right)\times 3\to \frac{15}{x-1}+\frac{3}{y-2}=6$

$\left(1\right)=\frac{6}{x-1}-\frac{3}{y-2}=1$

Add

____________________________

$\frac{21}{x-1}=7$

$21=7x-7$

$7x=28$

$x=4$

Put x in $\left(1\right)$

$\frac{6}{4-1}-\frac{3}{y-2}=1$

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

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

$y-2=3$

$y=5$.