Answer
$(z,z,z),\ \ z\in \mathbb{R}$
Work Step by Step
Write the augmented matrix and,
using row transformations arrive at the reduced row echelon form.
-----------
It was suggested to use technology for some problems...
Syntax for matrix input:
A:={{-1/2, 1, -1/2, 0},{ -1/2, -1/2, 1, 0},{ 1, -1/2, -1/2, 0}}
In the input box, begin typing "Red..."
select the function:
ReducedRowEchelonForm(A)
(see screenshot)
The last row contains all zeros, so the system is consistent.
With z as the parameter,
$x=z$
$y=z$
Solution: $(z,z,z),\ \ z\in \mathbb{R}$