# Use an inverse matrix to solve system of linear equations.x+2y=10x-2y=-6

Use an inverse matrix to solve system of linear equations.
$x+2y=10$
$x-2y=-6$

You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Step 1
Given system of equations is
$x+2y=10$
$x-2y=-6$
$AX=C$
$A=\left[\begin{array}{cc}1& 2\\ 1& -2\end{array}\right],X=\left[\begin{array}{c}x\\ y\end{array}\right],C=\left[\begin{array}{c}10\\ -6\end{array}\right]$
Step 2
The solution is given by
$X={A}^{-1}C$
$X=-\frac{1}{4}\left[\begin{array}{cc}-2& -2\\ -1& 1\end{array}\right]\left[\begin{array}{c}10\\ -6\end{array}\right]$
$X=-\frac{1}{4}\left[\begin{array}{cc}-20& 12\\ -10& -6\end{array}\right]\left[\begin{array}{c}2\\ 4\end{array}\right]$
$x=2,y=4$
Result:$x=2,y=4$