Answer
x = -5a
y = a
z = 3
Where a is any real number
Work Step by Step
The reduced row-echelon form of the matrix is:
$\begin{bmatrix}
1 & 5 & 0 & |0\\
0 & 0 & 1 & |3\\
0 & 0 & 0 & |0\\
0 & 0 & 0 & |0\\
\end{bmatrix}$
We can write the solution as:
x + 5y = 0
z = 3
We then can write the system in terms of y:
x = -5y
z = 3
To not use one of the variables in the system we can use a:
x = -5a
y = a
z = 3
Where a is any real number
