# Solve the following system of equations by using the inverse of the coefficient matrix A. (AX=B), x+5y=-10, -2x+7y=-31

Solve the following system of equations by using the inverse of the coefficient matrix A.
(AX=B), x+5y=-10, -2x+7y=-31
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$\left[\begin{array}{cc}1& 5\\ -2& 7\end{array}\right]\left\{\begin{array}{c}x\\ y\end{array}\right\}=\left\{\begin{array}{c}-10\\ -31\end{array}\right\}$
${A}^{-1}=\frac{1}{\left(1\ast 7\right)-\left(5\ast -2\right)}\left[\begin{array}{cc}7& -5\\ 2& 1\end{array}\right]=\frac{1}{17}\left[\begin{array}{cc}7& -5\\ 2& 1\end{array}\right]$