Question

Find '$m+n$' for the following simultaneous equations:
$3m+4n=7$
and $4m+3n=14$

Answer 1

$3m+4n=\mathrm{7..........}\left(1\right)$
$4m+3n=\mathrm{14........}\left(2\right)$
Adding equations $\left(1\right)$ and $\left(2\right)$
$3m+4n=7$
$4m+3n=14$
-------------------
$7m+7n=21$
$\therefore$ $7(m+n)=21$
$\therefore$ $m+n=\frac{21}{7}$
$\therefore$ $m+n=3$