#### Answer

The solution is $(-3, -7)$.

#### Work Step by Step

We can use the first equation to substitute for $y$ in the second equation. Then we can solve for $x$ first:
$x - 4 = 3x + 2$
Move the $x$ terms to the left side of the equation by subtracting $3x$ from each side of the equation:
$-2x - 4 = 2$
Move constants to the right side of the equation:
$-2x = 6$
Divide each side of the equation by $-2$ to solve for $x$:
$x = -3$
Now that we have the value for $x$, let's plug this value for $x$ into the first equation:
$y = -3 - 4$
Subtract to solve for $y$:
$y = -7$
The solution is $(-3, -7)$.