Question

solve the equation by cross multiplication
$x+ay=b$

$ax-by=c$

Answer 1

$x+ay=bax-by=c$

$wecanwrite$

$x+ay-b=0ax-by-c=0$

$then,bycrossmultiplication$

$\frac{x}{a\left(-c\right)-\left(-b\right)\left(-b\right)}$$=\frac{y}{\left(-b\right)\left(a\right)-\left(-c\right)\left(1\right)}$$=\frac{1}{\left(-b\right)\left(1\right)-\left(a\right)\left(a\right)}$

$\frac{x}{-ac-b^2}=\frac{y}{-ab+c}=\frac{1}{-b-a^2}$

$hence,x=\frac{ac+b^2}{b+a^2},y=\frac{-ab+c}{-b-a^2}$