Question

Solve, using cross-multiplication

$4x-y=55y-4x=7$

Answer 1

$\frac{x}{(b_1{c}_2-b_2{c}_1)}=\frac{y}{(c_1{a}_2-c_2{a}_1)}=\frac{1}{(a_1{b}_2-a_2{b}_1)}$

That means, $x=\frac{(b_1{c}_2-b_2{c}_1)}{(a_1{b}_2-a_2{b}_1)}y=\frac{(c_1{a}_2-c_2{a}_1)}{(a_1{b}_2-a_2{b}_1)}$

Given equations are $4x-y=5and5y-4x=7$

Comparing with $a_{1}x+b_{1}y+c_1=0and{a}_{2}x+b_{2}y+c_2=0$,

we have

$a_1=4,b_1=-1,c_1=-5and{a}_2=-4,b_2=5,c_2=-7$

$x=\frac{(-1)\times (-7)-5\times (-5))}{(4\times 5-(-4)\times (-1\left)\right)}y=\frac{(-5)\times (-4)-(-7)\times 4}{4\times 5-(-4)\times (-1)}x=\frac{7+25}{20-4}y=\frac{20+28}{20-4}x=2andy=3$