Answer
$m = 1$, $n = -4$
Work Step by Step
Given:
$3m + 4n = -13$
$5m + 6n = -19$
Multiply both sides of the first equation, $3m + 4n = -13$, by $3$:
$9m + 12n = -39$
Multiply both sides of the second equation, $5m + 6n = -19$ by $2$:
$10m + 12n = -38$
Subtract the first equation, $9m + 12n = -39$, from the second equation, $10m + 12n = -38$:
$10m + 12n - (9m + 12n) = -38 - (-39)$
$10m + 12n - (9m + 12n) = -38 + 39$
$10m + 12n - (9m + 12n) = 1$
Subtract each term of the binomial:
$10m - 9m + 12n - 12n = 1$
Combine like terms:
$m = 1$
Substitute $m = 1$ into the original first equation, $3m + 4n = -13$:
$3m + 4n = -13$:
$3(1) + 4n = -13$
$3 + 4n = -13$
Subtract $3$ from both sides:
$4n = -16$
Divide both sides by $4$:
$n = -4$
$m = 1$, $n = -4$
