Question

Solve the following system of equation by using the method of cross-multiplication.
$2x-y-3=0$
$4x+y-3=0$

Answer 1

The given system of equations is

$2x-y-3=0$

$4x+y-3=0$

By cross-multiplication, we have

$\Rightarrow \frac{x}{-1\times -3-1\times -3}=\frac{-y}{2\times -3-4\times -3}=\frac{1}{2\times 1-4\times -1}$

$\Rightarrow \frac{x}{3+3}=\frac{-y}{-6+12}=\frac{1}{2+4}$

$\Rightarrow \frac{x}{6}=\frac{y}{-6}=\frac{1}{6}$

$\Rightarrow x=\frac{6}{6}=1$ and $y=-\frac{6}{6}=-1$

Hence, the solution of the given system of equations is $x=1,y=-1$.