Question

Find the value of x and y using cross multiplication method:
$4x+3y=8$ and $6x+5y=13$

• A. $(\frac{1}{2},1)$
• B. $(\frac{1}{2},2)$
• C. $(\frac{1}{2},-1)$
• D. $(\frac{-1}{2},1)$

Answer 1

The correct option is B $(\frac{1}{2},2)$

$4x+3y=8$ ----- (1)
$6x+5y=13$ ----- (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.
$\frac{x}{3\times 13-5\times 8}=\frac{y}{8\times 6-4\times 13}=\frac{-1}{4\times 5-6\times 3}$
$\frac{x}{39-40}=\frac{y}{48-52}=\frac{-1}{20-18}$
$\frac{x}{-1}=\frac{y}{-4}=\frac{-1}{2}$
$\frac{x}{-1}=\frac{-1}{2}$
$x=\frac{1}{2}$
$\frac{y}{-4}=\frac{-1}{2}$
$y=\frac{4}{2}$
$y=2$
The solution is $(\frac{1}{2},2)$