Question

Find the value of m and n using cross multiplication method:
$3m+n=15$ and $m+2n=10$.

• A. (4, 3)
• B. (-4, 3)
• C. (-4, -3)
• D. (4, -3)

Answer 1

The correct option is A (4, 3)

$3m+n=15$ ----- (1)

$m+2n=10$ ----- (2)

First use formula for cross multiplication method:

$\frac{m}{b_1{c}_2-b_2{c}_1}=\frac{n}{c_1{a}_2-a_1{c}_2}=\frac{-1}{a_2{b}_2-a_2{b}_1}$

So, from equation (1) and (2) we can write the value of a, b and c.

$\frac{m}{1\times 10-2\times 15}=\frac{n}{15\times 1-3\times 10}=\frac{-1}{3\times 2-1\times 1}$

$\frac{m}{10-30}=\frac{n}{15-30}=\frac{-1}{6-1}$

$\frac{m}{-20}=\frac{n}{-15}=\frac{-1}{5}$

$\frac{m}{-20}=\frac{-1}{5}$

$m=\frac{20}{5}=4$

$\frac{n}{-15}=\frac{-1}{5}$

$n=\frac{15}{5}=3$

The solution is (4, 3)