Question

Find the value of $m$ and $n$ using elimination method:
$7m+6n=-37$ and $3m-2n=7$

• A. $(1,5)$
• B. $(-1,5)$
• C. $(1,-5)$
• D. $(-1,-5)$

Answer 1

The correct option is D $(-1,-5)$

$7m+6n=-37$
$3m-2n=7$
Multiply equation (2) by $3$ and then subtract the equation
$7m+6n=-37$
$9m-6n=21$
_____________
$16m=-16$
$\Rightarrow m=\frac{-16}{16}$
$\Rightarrow m=-1$
Put the value of $m=-1$ in equation (2), we get
$3m-2n=7$
$\Rightarrow 3(-1)-2n=7$
$\Rightarrow -3-7=2n$
$\Rightarrow -10=2n$
$\Rightarrow n=\frac{-10}{2}$
$\Rightarrow n=-5$
Therefore, the solution is $(-1,-5)$.