Question

Solve the following systems of equations:
$\frac{2}{x}+\frac{3}{y}=1$
$\frac{60}{x}+\frac{40}{y}=19,x\ne 0,y\ne 0$

Answer 1

Equation (1)$\times 30:\frac{60}{x}+\frac{90}{y}=30$

Equation (2)$\times 3:\frac{60}{x}+\frac{40}{y}=19$

Subtract two equations ;

$\Rightarrow \frac{50}{y}=11$

$\Rightarrow y=\frac{50}{11}$

Substitute y in equation 1 ;

$\Rightarrow x=\frac{100}{17}$