Answer
$$x = 3$$
Work Step by Step
The coefficients of the $y$ term differ only in sign, so if we add these equations without modification, we will cancel out the $y$ term and can then solve for $x$:
Let us add the equations. First, we cancel out the $y$ term:
$x + 3y = 6$
$x - 3y = 6$
_____________
$2x = 6$
$2x = 6$
Now we add both sides of the two equations to get:
$$4x = 12$$
Divide by $4$ to solve for $x$:
$$x = 3$$
