Question

Find the value of $x$ and $y$ using cross multiplication method:
$3x+5y=17$ and $2x+y=9$

• A. $(-4,1)$
• B. $(4,-1)$
• C. $(4,1)$
• D. $(-4,-1)$

Answer 1

Answer: (C)

$(4,1)$

$3x+5y=17$ ----- (1)

$2x+y=9$ ----- (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 $\frac{x}{5\times 9-1\times 17}=\frac{y}{17\times 2-3\times 9}=\frac{-1}{3\times 1-2\times 5}$

$\Rightarrow \frac{x}{45-17}=\frac{y}{34-27}=\frac{-1}{3-10}$

$\Rightarrow \frac{x}{28}=\frac{y}{7}=\frac{-1}{-7}$

$\Rightarrow \frac{x}{28}=\frac{-1}{-7}$

$\Rightarrow x=\frac{-28}{-7}=4$

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

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

The solution is$(4,1)$.