Question

solve the system of equations using the linear combination method.\

$$\begin{cases} 5m + 3n = 41 \\\\ 3m - 6n = 9 \\end{cases}$$

\
enter your answers in the boxes.\
m = \square\
n = \square

Explanation:

Step1: Eliminate $n$ via scaling

Multiply first equation by 2:
$2(5m + 3n) = 2(41) \implies 10m + 6n = 82$

Step2: Add equations to cancel $n$

Add scaled eq to second eq:
$(10m + 6n) + (3m - 6n) = 82 + 9$
$13m = 91$

Step3: Solve for $m$

Divide both sides by 13:
$m = \frac{91}{13} = 7$

Step4: Substitute $m$ to find $n$

Plug $m=7$ into $3m - 6n = 9$:
$3(7) - 6n = 9 \implies 21 - 6n = 9$
$-6n = 9 - 21 = -12$
$n = \frac{-12}{-6} = 2$

Answer:

$m = 7$
$n = 2$