Question

Find the value of x and y using cross multiplication method:
$5x+2y=32$ and $6x+6y=42$

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

Answer 1

The correct option is B $(6,1)$

$5x+2y=32$ ----- (1)

$6x+6y=42$ ----- (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.

$\frac{x}{2\times 42-6\times 32}=\frac{y}{32\times 6-5\times 42}=\frac{-1}{5\times 6-6\times 2}$

$\frac{x}{84-192}=\frac{y}{192-210}=\frac{-1}{30-12}$

$\frac{x}{108}=\frac{y}{-18}=\frac{-1}{18}$

$\frac{x}{-108}=\frac{-1}{18}$

$x=\frac{108}{18}=6$

$\frac{y}{-18}=\frac{-1}{18}$

$y=\frac{18}{18}=1$

The solution is (6, 1)