Question

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

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

Answer 1

The correct option is C (1, -1)

$2x-y=3$ ----- (1)
$4x+y=3$ ----- (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.
$\frac{x}{(-1)\times 3-\left(1\right)\times 3}=\frac{y}{3\times 4-2\times 3}=\frac{-1}{2\times \left(1\right)-4\times (-1)}$
$\frac{x}{-3-3}=\frac{y}{12-6}=\frac{-1}{2+4}$
$\frac{x}{-6}=\frac{y}{6}=\frac{-1}{6}$
$\frac{x}{-6}=\frac{-1}{6}$
$x=\frac{6}{6}=1$
$\frac{y}{6}=\frac{-1}{6}$
$y=\frac{-6}{6}$
$y=-1$
The solution is (1, -1)