Question

Find the value of x and y using cross multiplication method:
$x-2y=1$ and $x+4y=6$

• A. $(\frac{8}{3},\frac{5}{6})$
• B. $(\frac{-8}{3},\frac{5}{6})$
• C. $(\frac{8}{3},\frac{-5}{6})$
• D. $(\frac{-8}{3},\frac{-5}{6})$

Answer 1

The correct option is A $(\frac{8}{3},\frac{5}{6})$

$x-2y=1$ ----- (1)
$x+4y=6$ ----- (2)
First use formula for cross multiplication method:
$\frac{x}{b_1{c}_2-b_2{c}_1}=\frac{y}{c_1{a}_2-a_1{c}_2}=\frac{-1}{a_1{b}_2-a_2{b}_1}$
So, from equation (1) and (2) we can write the value of a, b and c.
$\frac{x}{-2\times 6-4\times 1}=\frac{y}{1\times 1-1\times 6}=\frac{-1}{1\times 4-1\times -2}$
$\frac{x}{-12-4}=\frac{y}{1-6}=\frac{-1}{4+2}$
$\frac{x}{-16}=\frac{y}{-5}=\frac{-1}{6}$
$\frac{x}{-16}=\frac{-1}{6}$
$x=\frac{16}{6}=\frac{8}{3}$
$\frac{y}{-5}=\frac{-1}{6}$
$y=-1\times \frac{-5}{6}$
$y=\frac{5}{6}$
The solution is $(\frac{8}{3},\frac{5}{6})$