# Solve the system of linear equations using matrices.3x-2y-4=02y=12-x

Solve the system of linear equations using matrices.
$3x-2y-4=0$
$2y=12-x$

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STEP 1
System of linear equation
$3x-2y=4$
$x+2y=12$
Augmented matrix is
$\left[\begin{array}{cccc}3& -2& |& 4\\ 1& 2& |& 12\end{array}\right]$
Reduring the matrix to reduced
Row echelon form by
Row operations
${R}_{1}\to \frac{1}{3}R$
$\left[\begin{array}{cccc}1& \frac{-2}{3}& |& \frac{4}{3}\\ 1& 2& |& 12\end{array}\right]$
${R}_{2}\to {R}_{2}-{R}_{1}$
$\left[\begin{array}{cccc}1& \frac{-2}{3}& |& \frac{4}{3}\\ 0& \frac{8}{3}& |& \frac{32}{3}\end{array}\right]$
${R}_{2}\to \frac{8}{3}{R}_{2}$
$\left[\begin{array}{cccc}1& \frac{-2}{3}& |& \frac{4}{3}\\ 0& 1& |& 4\end{array}\right]$
Step2
${R}_{1}\to {R}_{1}+\frac{2}{3}{R}_{2}$
$\left[\begin{array}{cccc}1& 0& |& 4\\ 0& 1& |& 4\end{array}\right]$
$⇒x=4$
$y=4$
Thus solution of system is $x=4,y=4$

Jeffrey Jordon