Answer
$x= 8$
$y= 1$
$z = 0$
$w = 3$
Work Step by Step
Given:
$x + y - 3w = 0$
$x - 2z = 8$
$2y - z +w = 5$
$2x + 3y - 2w = 13$
The question asks for a graphing calculator to solve the system of equations. The calculations were done on desmos.com/matrix
Convert the linear system into a matrix equation.
Below shows A and B as a matrix equation from the linear system:
$A=\left[\begin{array}{ll}
1 & 1 & 0 & -3\\
1 & 0 & -2 & 0\\
0 & 2 & -1 & 1\\
2 & 3 & 0 & -2
\end{array}\right]$
$B=\left[\begin{array}{l}
0\\
8\\
5\\
13
\end{array}\right]$
Then the calculator finds the inverse of A (see $A^{-1}$ below)
To determine matrix X, the solution, multiply the inverse of A by B (see $A^{-1}B$ below)
The answers are below:
$x= 8$
$y= 1$
$z = 0$ (on desmos, it displays a number that is very close to zero)
$w = 3$