#### Answer

This system of equations has no solution.

#### Work Step by Step

Let's solve one of the equations for one of the variables, and then use that equation to substitute into the other equation. Let's solve the first equation for $y$:
$3x + y = 4$
Subtract $3x$ from each side of the equation to solve for $y$:
$y = -3x + 4$
We can use this equation to substitute for $y$ in the second equation. Then we can solve for $x$ first:
$-6x - 2(-3x + 4) = 12$
Use distribution to get rid of the parentheses:
$-6x + 6x - 8 = 12$
Combine the $x$ terms:
$-8 = 12$
This statement is false for every value of $x$; therefore, this system of equations has no solution.