Question

Solve the following pairs of linear equation:

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

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

Answer 1

Let $a=\frac{1}{x},b=\frac{1}{y}$

$\Rightarrow 2a+\frac{2}{3}b=\frac{1}{6}.....\left(i\right)$ and

$2a-b=1$

$\Rightarrow 2a=1+b$

Put in $\left(i\right)$

$\Rightarrow 1+b+\frac{2}{3}b=\frac{1}{6}$

$\Rightarrow 1+\frac{5}{3}b=\frac{1}{6}$

$\Rightarrow \frac{5}{3}b=-\frac{5}{6}$

$\Rightarrow b=-\frac{1}{2}⟹a=\frac{1}{4}$

$\therefore x=4,y=-2$