Question

Find the value of x and y using cross multiplication method:
$6x-5y=9$ and $5x-6y=2$

• A. $(4,3)$
• B. $(5,3)$
• C. $(4,-3)$
• D. $(-4,3)$

Answer 1

Answer: (A)

$(4,3)$

$6x-5y=9$ ----- (1)
$5x-6y=2$ ----- (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.
$\frac{x}{(-5)\times 2-(-6)\times 9}=\frac{y}{9\times 5-6\times 2}=\frac{-1}{6\times (-6)-5\times (-5)}$
$\frac{x}{-10+54}=\frac{y}{45-12}=\frac{-1}{-36+25}$
$\frac{x}{44}=\frac{y}{33}=\frac{-1}{-11}$
$\frac{x}{44}=\frac{-1}{-11}$
$x=\frac{-44}{-11}=-3$
$\frac{y}{33}=\frac{-1}{-11}$
$y=\frac{-33}{-11}$
$y=3$
The solution is $(4,3)$