Question

Find the value of x and y using cross multiplication method:
$x+6y=32$ and $x+3y=17$

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

Answer 1

The correct option is D (2, 5)

$x+6y=32$ ----- (1)

$x+3y=17$ ----- (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.

$\frac{x}{6\times 17-3\times 32}=\frac{y}{32\times 1-1\times 17}=\frac{-1}{1\times 3-1\times 6}$

$\frac{x}{102-96}=\frac{y}{32-17}=\frac{-1}{3-6}$

$\frac{x}{6}=\frac{y}{15}=\frac{-1}{-3}$

$\frac{x}{6}=\frac{-1}{-3}$

$x=\frac{-6}{-3}=2$

$\frac{y}{15}=\frac{-1}{-3}$

$y=\frac{-15}{-3}=5$

The solution is (2, 5)