Question

Solve the following pair of equations by cross-multiplication method:
$2x-5y=4;3x-8y=5$

Answer 1

Representing the given equations in standard form
$2x-5y=4\Rightarrow 2x-5y-4=\mathrm{0........}\left(1\right)$
$3x-8y=5\Rightarrow 3x-8y-5=\mathrm{0.........}\left(2\right)$
Using cross-multiplication method to solve the above equations
$\frac{x}{(-5)(-5)-(-8)(-4)}=\frac{y}{(-4)\left(3\right)-(-5)\left(2\right)}=\frac{1}{\left(2\right)(-8)-\left(3\right)(-5)}$
$⟹\frac{x}{25-32}=\frac{y}{-12+10}=\frac{1}{-16+15}$
$\frac{x}{-7}=\frac{y}{-2}=\frac{1}{-1}$
$x=\frac{-7}{-1}=7;y=\frac{-2}{-1}=2$
Solution is $(x,y)=(7,2)$