Answer
$(1-4t, -1-t, t)$
Work Step by Step
Step 1. Set up the augmented matrix of the system of equations:
$\begin{array} \\A=\\ \end{array}
\begin{bmatrix} 1&-3&1&4\\ 4&-1&15&5 \end{bmatrix}
\begin{array} \\ \\R_2-4R_1\to R_2\\ \end{array}$
Step 2. Do the row operations indicated on the right side of the matrix:
$\begin{array} \\A=\\ \end{array}
\begin{bmatrix} 1&-3&1&4\\ 0&11&11&-11 \end{bmatrix}
\begin{array} \\ \\ \\ \end{array}$
Step 3. Let $z=t$, the last row gives $y+t=-1$ or $y=-1-t$, use row-1 to get $x-3(-1-t)+t=4$ or $x=1-4t$
Step 4. Conclusion: the solutions are $(1-4t, -1-t, t)$
