Question

Solve the following systems of equations:
$x+y=5xy$
$3x+2y=13xy,$
$x\ne 0,y\ne 0$

Answer 1

Divide by 'xy' in both equations ;

$\Rightarrow \frac{1}{x}+\frac{1}{y}=5$

$\Rightarrow \frac{3}{x}+\frac{2}{y}=13$

Multiply equation (1) by 3 ;

$\Rightarrow \frac{3}{x}+\frac{3}{y}=15$

$\Rightarrow \frac{3}{x}+\frac{2}{y}=13$

Subtract two equations ;

$\Rightarrow \frac{1}{y}=2$

$\Rightarrow y=\frac{1}{2}$

Substituting in either equation, we get ;

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