# Solve the systems of equations using matrices.4x+5y=83x-4y=3Leave answer in fraction form.4x+y+z=3-x+y=-11+2z2y+2z=-1-x

Solve the systems of equations using matrices.
$4x+5y=8$
$3x-4y=3$
$4x+y+z=3$
$-x+y=-11+2z$
$2y+2z=-1-x$

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Step 1
The given equation
$4x+5y=8$
$3x-4y=3$
In matrix form
$\left[\begin{array}{cc}4& 5\\ 3& -4\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}8\\ 3\end{array}\right]$ $AX=B$

Step 2

$X={A}^{-1}BA=\left[\begin{array}{cc}4& 5\\ 3& -4\end{array}\right]{A}^{-1}=\frac{1}{-16-15}\left[\begin{array}{cc}-4& -5\\ -3& 4\end{array}\right]=\frac{-1}{31}\left[\begin{array}{cc}-4& -5\\ -3& 4\end{array}\right]$
$B=\left[\begin{array}{c}8\\ 3\end{array}\right]$
Step 3
${A}^{-1}B=\frac{-1}{31}\left[\begin{array}{cc}-4& -5\\ -3& 4\end{array}\right]$$\left[\begin{array}{c}8\\ 3\end{array}\right]$
$=\frac{-1}{31}\left[\begin{array}{c}-47\\ -12\end{array}\right]$
$x=\frac{47}{31}$
$y=\frac{12}{31}$

Jeffrey Jordon