#### Answer

$c = 22$
$d = 4$

#### Work Step by Step

$c = 3d+10$
$c = 2d + 14$
1. Rewrite one equation to isolate for $d$
$c = 2d + 14$
$c - 14 = 2d$
$d = \frac{c-14}{2}$
2. Substitute the previous equation for $d$ into the first equation. Solve for $c$.
$c = 3(\frac{c-14}{2}) + 10$
$c = \frac{3c-42}{2} + 10$
$2c = 3c-42 + 20$
$2c - 3c = - 42 + 20$
$-c = - 22$
$c = 22$
3. Substitute $c$ back into any of the equations to solve for $d$
$c = 2d + 14$
$c - 14 = 2d$
$d = \frac{(22)-14}{2}$
$d = \frac{8}{2}$
$d = 4$
Check:
$c = 3d + 10$
$22 \overset{?}{=} 3(4) + 10$
$22 \overset{?}{=} 12 + 10$
$22 = 22$