Question

Find the value of $x$ and $y$ using cross multiplication method:
$6x+y=18$ and $5x+2y=22$

• A. $(-2,6)$
• B. $(2,6)$
• C. $(2,-6)$
• D. $(-2,-6)$

Answer 1

Answer: (B)

$(2,6)$

$6x+y=18$ ....(1)

$5x+y=8$ ....(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$c$.

Thus $\frac{x}{1\times 22-2\times 18}=\frac{y}{18\times 5-6\times 22}=\frac{-1}{6\times 2-5\times 1}$

$\Rightarrow \frac{x}{22-36}=\frac{y}{90-132}=\frac{-1}{12-5}$

$\Rightarrow \frac{x}{-14}=\frac{y}{-42}=\frac{-1}{7}$

$\Rightarrow \frac{x}{-14}=\frac{-1}{7}$

$\Rightarrow x=\frac{14}{7}=2$

$\Rightarrow \frac{y}{-42}=\frac{-1}{7}$

$\Rightarrow y=\frac{42}{7}=6$

The solution is $(2,6)$.