Question

Solve $4m+6n=54$ and $3m+2n=28$.

Answer 1

$4m+6n=54$ (1)

$3m+2n=28$ (2)

Multiplying (1) by 3 and (2) by 4

$12m+18n=162$ (3)

$12m+8n=112$ (4)

Subtracting (4) from (3)

$10n=50$

$n=\frac{50}{10}=5$ (5)

Substituting (5) in (1)

$4m+6\left(5\right)=54$

$4m=54-30$

$4m=24$

$m=6$

Hence $m=6$ and $n=5$