Question

Find the value of $x$ and $y$ using cross multiplication method:
$3x+4y=33$ and $6x+3y=36$

• A. $(3,6)$
• B. $(3,-6)$
• C. $(-3,-6)$
• D. $(-3,6)$

Answer 1

The correct option is A $(3,6)$

$3x+4y=33$ .....(1)

$6x+3y=36$ .....(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 $c$.

Therefore, $\frac{x}{4\times 36-3\times 33}=\frac{y}{33\times 6-3\times 36}=\frac{-1}{3\times 3-6\times 4}$

$\Rightarrow \frac{x}{144-99}=\frac{y}{198-108}=\frac{-1}{9-24}$

$\Rightarrow \frac{x}{45}=\frac{y}{90}=\frac{-1}{-15}$

$\Rightarrow \frac{x}{45}=\frac{-1}{-15}$

$\Rightarrow x=\frac{-45}{-15}=3$

$\Rightarrow \frac{y}{90}=\frac{-1}{-15}$

$\Rightarrow y=\frac{-90}{-15}=6$

The solution is $(3,6)$.