Question

Solve the following systems of equations by the method of cross-multiplication:
$\frac{x+y}{xy}=2,\frac{x-y}{xy}=6$

Answer 1

Equation (1) : $\frac{1}{x}+\frac{1}{y}-2=0$

Equation (2) : $\frac{1}{x}-\frac{1}{y}+6=0$

By method of cross multiplication :

$\Rightarrow \frac{1/x}{(1\times 6)-(-1\times -2)}=\frac{1/y}{(-2\times 1)-(6\times 1)}=\frac{1}{(1\times -1)-(1\times 1)}$

$\Rightarrow 1/x=\frac{4}{-2}=-2$

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

$\Rightarrow 1/y=\frac{-8}{-2}=4$

$\Rightarrow y=\frac{1}{4}$