Question

Find the value of x and y using cross multiplication method:
$3x-5y=-1$ and $x+2y=-4$

• A. (2, 1)
• B. (-2, 1)
• C. (2, -1)
• D. (-2, -1)

Answer 1

The correct option is D (-2, -1)

$3x-5y=-1$ ----- (1)

$x+2y=-4$ ----- (2)

First use formula for cross multiplication method:

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

So, from equation (1) and (2) we can write the value of a, b and c.

$\frac{x}{(-5)\times (-4)-2\times (-1)}=\frac{y}{(-1)\times 1-3\times (-4)}=\frac{-1}{3\times 2-1\times (-5)}$

$\frac{x}{20+2}=\frac{y}{-1+12}=\frac{-1}{6+5}$

$\frac{x}{22}=\frac{y}{11}=\frac{-1}{11}$

$\frac{x}{22}=\frac{-1}{11}$

$x=\frac{-22}{11}=-2$

$\frac{y}{11}=\frac{-1}{11}$

$y=\frac{-11}{11}$

$y=-1$

The solution is (-2, -1)