Answer
$m = 2, n = 3$
Work Step by Step
Rewrite the first equation so that $n$ is isolated on the left side of the equation. Subtract $5m$ from each side of the equation:
$$-n = -5m + 7$$
Divide both sides of the equation by $-1$ to isolate $n$:
$$n = 5m - 7$$
Use this expression to substitute for $n$ in the second equation:
$$3 + 3(5m - 7) = 6m$$
Multiply to simplify:
$$3 + 15m - 21 = 6m$$
Subtract $15m$ from each side of the equation:
$$3 - 21 = -9m$$
Combine like terms:
$$-18 = -9m$$
Divide each side of the equation by $-9$:
$$m = 2$$
Use this value for $m$ to substitute into the first equation to solve for $n$:
$$5(2) - n = 7$$
Multiply to simplify:
$$10 - n = 7$$
Subtract $10$ from each side of the equation:
$$-n = -3$$
Divide each side of the equation by $-1$:
$$n = 3$$
