# System of equations. Use matrices to solve 2x+y=-10 6x-3y=6

System of equations. Use matrices to solve
2x+y=-10
6x-3y=6
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Laith Petty
Step 1
Consider the following system of linear equations:
2x+y=-10
6x−3y=6
Rewrite the system in the form of augmented matrix:
$\left[\begin{array}{ccc}2& 1& -10\\ 6& -3& 6\end{array}\right]$
${R}_{1}\to \frac{1}{2}{R}_{1}$
$\left[\begin{array}{ccc}1& \frac{1}{2}& -5\\ 6& -3& 6\end{array}\right]$
Step 2
${R}_{2}\to {R}_{2}-6{R}_{1}$
$\left[\begin{array}{ccc}2& \frac{1}{2}& -5\\ 0& -6& 36\end{array}\right]$
${R}_{2}\to \frac{-1}{6}{R}_{2}$
$\left[\begin{array}{ccc}1& \frac{1}{2}& -5\\ 0& 1& -6\end{array}\right]$
Step 3
${R}_{1}\to {R}_{1}-\frac{1}{2}{R}_{2}$
$\left[\begin{array}{ccc}1& 0& -2\\ 0& 1& -6\end{array}\right]$
x=−2
y=−6
Hence, the solution is x=−2 and y=−6.
Jeffrey Jordon