Question

Solve the following system of equations by cross-multiplication method.
2x + 3y + 8 = 0
4x + 5y + 14 = 0

Answer 1

The given system of equations is
2x + 3y + 8 = 0
4x + 5y + 14 = 0
By cross-multiplication, we get



$\Rightarrow$ $\frac{x}{3\times 14-5\times 8}=\frac{-y}{2\times 14-4\times 8}=\frac{1}{2\times 5-4\times 3}$
$\Rightarrow$ $\frac{x}{42-40}=\frac{-y}{28-32}=\frac{1}{10-12}$
$\Rightarrow$ $\frac{x}{2}=\frac{-y}{-4}=\frac{1}{-2}$
$\Rightarrow$ $\frac{x}{2}=\frac{1}{-2}$
$\Rightarrow$ $x=-1$
and $\frac{-y}{-4}=\frac{1}{-2}\Rightarrow y=-2$