Question

Find the value of $x$ and $y$ using cross multiplication method:
$2x+y=13$ and $x+y=8$

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

Answer 1

The correct option is A $(5,3)$

$2x+y=13$ ....(1)

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

Therefore, $\frac{x}{1\times 8-1\times 13}=\frac{y}{13\times 1-2\times 8}=\frac{-1}{2\times 1-1\times 1}$

$\Rightarrow \frac{x}{8-13}=\frac{y}{13-16}=\frac{-1}{2-1}$

$\Rightarrow \frac{x}{-5}=\frac{y}{-3}=\frac{-1}{1}$

$\Rightarrow \frac{x}{-5}=\frac{-1}{1}$

$\Rightarrow x=\frac{5}{1}=5$

$\Rightarrow \frac{y}{-3}=\frac{-1}{1}$

$\Rightarrow y=\frac{3}{1}=3$

The solution is $(5,3)$.