Question

Solve the simultaneous equations:
$\frac{1}{x}+\frac{1}{y}=12,\frac{3}{x}-\frac{2}{y}=1$

Answer 1

$\frac{1}{x}+\frac{1}{y}=12$
$\frac{3}{x}-\frac{2}{y}=1$
Substituting $\frac{1}{x}=a$ and $\frac{1}{y}=b$ in the above equations,
$a+b=12...\left(1\right)$
$3a-2b=1...\left(2\right)$
Multiplying equations $\left(1\right)$ by $2$ and solving with $\left(2\right)$, we get
$2a+2b=24...\left(3\right)$
$\underset{–}{3a-2b=1}$
$5a=25$
$a=\frac{25}{5}=5$
Substituting, $a=5$ in equation $\left(1\right)$,
$a+b=12$
$5+b=12$
$b=12-5=7$