I am trying to convert the parametric equation of a plane in $\mathbb{R}^3$ containing 3 points: $\left[\begin{matrix} 0\\ 1\\ 3 \end{matrix}\right] $, $\left[\begin{matrix} 5\\ 1\\ 4 \end{matrix}\right] $, $\left[\begin{matrix} 6\\ 1\\ 2 \end{matrix}\right] $, to a cartesian equation.
The parametric equation I believe is: $\left[\begin{matrix} 0\\ 1\\ 3 \end{matrix}\right] + s\left[\begin{matrix} 5\\ 0\\ 1 \end{matrix}\right] + t\left[\begin{matrix} 6\\ 0\\ -1 \end{matrix}\right] $ with $s, t \in \mathbb{R}$
Following this:
$x = 5s + 6t$
$y = 1$
$z = 3 + s - t$
I am unsure how to proceed, as I am not able to eliminate both $s$ and $t$.