Question

Find the value of x and y using cross multiplication method:
$2x+2y=18$ and $x+3y=17$

• A. (5, -4)
• B. (-5, 4)
• C. (5, 4)
• D. (-5, -2)

Answer 1

The correct option is C (5, 4)

$2x+2y=18$ ----- (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.

$\frac{x}{2\times 17-3\times 18}=\frac{y}{18\times 1-2\times 17}=\frac{-1}{2\times 3-1\times 2}$

$\frac{x}{34-54}=\frac{y}{18-34}=\frac{-1}{6-2}$

$\frac{x}{-20}=\frac{y}{-16}=\frac{-1}{4}$

$\frac{x}{-20}=\frac{-1}{4}$

$x=\frac{20}{4}=5$

$\frac{y}{-16}=\frac{-1}{4}$

$y=\frac{16}{4}=4$

The solution is (5, 4)