#### Answer

$x_{1} = -t$
$x_{2} = 0$
$x_{3} = t$
$t$ is any real number.

#### Work Step by Step

From Equation 2, we can conclude that $x_2 = 0$.
Substituting this value into Equation 1 results in the following.
$x_{1} + 0x_{2} + x_{3} = 0$
$0x_{1} + x_2 = 0$.
We can see that there are 2 pivots and that $x_3$ is a free variable.
Therefore, $x_{3} = t$ where $t$ is any real number.
We can then substitute this value into Equation 1 and then solve for $x_1$.
$x_1 = -t$
$x_2 = 0$
$x_3 = t$