Question

Find the value of x and y using cross multiplication method:
$15x+11y=-23$ and $-2x+7y=20$

• A. $(3,2)$
• B. $(-3,2)$
• C. $(3,-1)$
• D. $(3,1)$

Answer 1

Answer: (B)

$(-3,2)$

$15x+11y=-23$ ----- (1)
$-2x+7y=20$ ----- (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.
$\frac{x}{11\times 20-7\times (-23)}=\frac{y}{(-23)\times (-2)-15\times 20}=\frac{-1}{15\times 7-(-2)\times 11}$
$\frac{x}{220+161}=\frac{y}{46-300}=\frac{-1}{105+22}$
$\frac{x}{381}=\frac{y}{-254}=\frac{-1}{127}$
$\frac{x}{381}=\frac{-1}{127}$
$x=\frac{-381}{127}=-3$
$\frac{y}{-254}=\frac{-1}{127}$
$y=\frac{254}{127}$
$y=2$
The solution is $(-3,2)$.