Question

Find the value of x and y using cross multiplication method:
$5x+8y=9$ and $2x+3y=4$

• A. (5, 2)
• B. (-5, 2)
• C. (5, 7)
• D. (5, -2)

Answer 1

Answer: (D)

(5, -2)

$5x+8y=9$ ----- (1)

$2x+3y=4$ ----- (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.

$\frac{x}{8\times 4-3\times 9}=\frac{y}{9\times 2-5\times 4}=\frac{-1}{5\times 3-2\times 8}$

$\frac{x}{32-27}=\frac{y}{18-20}=\frac{-1}{15-16}$

$\frac{x}{5}=\frac{y}{-2}=\frac{-1}{-1}$

$\frac{x}{5}=\frac{-1}{-1}$

$x=\frac{-5}{-1}=5$

$\frac{y}{-2}=\frac{-1}{-1}$

$y=\frac{2}{-1}=-2$

The solution is (5, -2)