Question

Find the value of x and y using cross multiplication method:
$x+2y=8$ and $2x-3y=2$

• A. (4, 2)
• B. (-4, 2)
• C. (6, -1)
• D. (4, 1)

Answer 1

The correct option is A (4, 2)

$x+2y=8$ ----- (1)
$2x-3y=2$ ----- (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.
$\frac{x}{2\times 2-(-3)\times 8}=\frac{y}{8\times 2-1\times 2}=\frac{-1}{1\times (-3)-2\times 2}$
$\frac{x}{4+24}=\frac{y}{16-2}=\frac{-1}{-3-4}$
$\frac{x}{28}=\frac{y}{14}=\frac{-1}{-7}$
$\frac{x}{28}=\frac{-1}{-7}$
$x=\frac{-28}{-7}=4$
$\frac{y}{14}=\frac{-1}{-7}$
$y=\frac{-14}{-7}$
$y=2$
The solution is (4, 2)