Question

Solve the following system of equation by using the method of cross-multiplication.
$2x+y-35=0$
$3x+4y-65=0$

Answer 1

The given system of equations is

$2x+y-35=0$

$3x+4y-65=0$

$\Rightarrow \frac{x}{1\times -65-4\times -35}=\frac{-y}{2\times -65-3\times -35}=\frac{1}{2\times 4-3\times 1}$

$\Rightarrow \frac{x}{-65+140}=\frac{-y}{-130+105}=\frac{1}{8-3}$

$\Rightarrow \frac{x}{75}=\frac{y}{25}=\frac{1}{5}\Rightarrow x=\frac{75}{5}=15$ and $y=\frac{25}{5}=5$

Hence, the solution of the given system of equations is $x=15,y=5$.