Question

Solve the following system of equation by using the method of cross-multiplication.
$2x+3y=17$
$3x-2y=6$

Answer 1

The given system of equations is

$2x+3y-17=0$

$3x-2y-6=0$

By cross-multiplication, we have

$\Rightarrow \frac{x}{3\times -6-(-2)\times -17}=\frac{-y}{2\times -6-3\times -17}=\frac{1}{2\times -2-3\times 3}$

$\Rightarrow \frac{x}{-18-34}=\frac{-y}{-12+51}=\frac{1}{-4-9}$

$\Rightarrow \frac{x}{-52}=\frac{-y}{39}=\frac{1}{-13}$

$\Rightarrow x=\frac{-53}{-13}$ and $y=\frac{-39}{-13}\Rightarrow x=4$ and $y=3$

Hence, $x=4,y=3$ is the solution to the given system of equations.