Answer
$(-2+z,-4+2z,z),\ \ z\in \mathbb{R}$
Work Step by Step
Write the augmented matrix and,
using row transformations arrive at the reduced row echelon form.
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It was suggested to use technology for some problems...
Syntax for matrix input:
A:={{1, -1/2, 0, 0},{ 1/2, 0, -1/2, -1},{ 3, -1, -1, -2}}
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,
$x=-2+z$
$y=-4+2z$
Solution: $(-2+z,-4+2z,z),\ \ z\in \mathbb{R}$
