Question

Find the value of $x$ and $y$ using cross multiplication method:
$4x+3y=29$ and $6x+3y=39$

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

Answer 1

Answer: (B)

$(5,3)$

$4x+3y=29$ ----- (1)

$6x+3y=39$ ----- (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 $\left(1\right)$ and $\left(2\right)$ we can write

$\frac{x}{3\times 39-3\times 29}=\frac{y}{29\times 6-4\times 39}=\frac{-1}{4\times 3-6\times 3}$

$\frac{x}{117-87}=\frac{y}{174-156}=\frac{-1}{12-18}$

$\frac{x}{30}=\frac{y}{18}=\frac{-1}{-6}$

$\frac{x}{30}=\frac{-1}{-6}$

$x=\frac{-30}{-6}=5$

$\frac{y}{18}=\frac{-1}{-6}$

$y=\frac{-18}{-6}=3$

Thus the required solution is $(5,3)$