Question

Solve by cross multiplication method:
$4x-5y=-7$
$4x-y=5$

• A. $x=-2,y=2$
• B. $x=3,y=-2$
• C. $x=2,y=3$
• D. $x=-2,y=-2$

Answer 1

The correct option is C $x=2,y=3$

Given equation are

$4x-5y+7=0$

$4x-y-5=0$

Comparing that equation

$a_{1}x+b_{1}y+c_1=0$

$a_{2}x+b_{2}y+c_2=0$

Then,

$a_1=4,b_1=-5,c_1=7$

$a_2=4,b_2=-1,c_2=-5$

By cross multiplication method,

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

$\frac{x}{(-5)(-5)-(-1)\left(7\right)}=\frac{y}{\left(7\right)\left(4\right)-(-5)\left(4\right)}=\frac{1}{\left(4\right)(-1)-\left(4\right)(-5)}$

$\frac{x}{25+7}=\frac{y}{28+20}=\frac{1}{-4+20}$

$\frac{x}{32}=\frac{y}{48}=\frac{1}{16}$

$x=\frac{32}{16}$ and $y=\frac{48}{16}=3$

$x=2$ and $y=3$