Question

Find the value of $x$ and $y$ using cross multiplication method:
$5x+y=15$ and $2x+6y=34$

• A. $(-2,5)$
• B. $(2,-5)$
• C. $(2,5)$
• D. $(-2,-5)$

Answer 1

Answer: (C)

$(2,5)$

$5x+y=15$ .....(1)

$2x+6y=34$ ....(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 $\frac{x}{1\times 34-6\times 15}=\frac{y}{15\times 2-5\times 34}=\frac{-1}{5\times 6-2\times 1}$

$\Rightarrow \frac{x}{34-90}=\frac{y}{30-170}=\frac{-1}{30-2}$

$\Rightarrow \frac{x}{-56}=\frac{y}{-140}=\frac{-1}{28}$

$\Rightarrow \frac{x}{-56}=\frac{-1}{28}$

$\Rightarrow x=\frac{56}{28}=2$

$\Rightarrow \frac{y}{-140}=\frac{-1}{28}$

$\Rightarrow y=\frac{140}{28}=5$

The solution is $(2,5)$.