Question

Find '$m+n$' for the following simultaneous equations : $7m+3n=12$ and $3m+7n=8$.

Answer 1

Let $7m+3n=12$ ...(1)
and $3m+7n=8$ ...(2)
From equation (2), find the value of $m$ in terms of $n$
$m=\frac{8-7n}{3}$ ...(3)
Substituting $m=\frac{8-7n}{3}$ in equation (1)
$\Rightarrow$ $7\left(\frac{8-7n}{3}\right)+3n=12$
$\Rightarrow \frac{56}{3}-\frac{49n}{3}+3n=12$
$\Rightarrow \frac{-49n}{3}+3n=12-\frac{56}{3}$
$\Rightarrow \frac{-40n}{3}=\frac{-20}{3}$
$\Rightarrow n=\frac{-20}{-40}$
$\Rightarrow n=\frac{1}{2}$
Substituting $n=\frac{1}{2}$ in equation (3), we get
$m=\frac{8-7\left(\frac{1}{2}\right)}{3}$
$\Rightarrow m=\frac{\frac{9}{2}}{3}$
$\Rightarrow m=\frac{9}{6}$
$\Rightarrow m=\frac{3}{2}$
Therefore, the value of $m+n$ is $\frac{3}{2}+\frac{1}{2}=\frac{4}{2}=2$.