Question

Solve the following system of equations for $x$ & $y$.
$\frac{5}{x-1}+\frac{1}{y-2}=2,\frac{3}{x-1}=1$

Answer 1

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

$\Rightarrow 3=x-1$

$\Rightarrow x=4$

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

$\frac{5}{4-1}+\frac{1}{y-2}=2$

$\frac{1}{y-2}=2-\frac{5}{3}$

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

$\Rightarrow y-2=3$

$\Rightarrow y=5$