# 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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umshikepl
${A}^{-1}=\frac{1}{|A|}adjA$
$=\frac{1}{17}\left[\begin{array}{cc}7& -5\\ 2& 1\end{array}\right]$
$=\left[\begin{array}{cc}\frac{7}{17}& \frac{-5}{17}\\ \frac{2}{17}& \frac{1}{17}\end{array}\right]$
AX=B
$X={A}^{-1}B$
$\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}\frac{85}{17}\\ \frac{-51}{17}\end{array}\right)$
$=\left(\begin{array}{c}5\\ -3\end{array}\right)$
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on2t1inf8b
$AX=B⇒X=A-1BA=,B=\left(\begin{array}{c}-10\\ -31\end{array}\right)$ and X=
${A}^{-1}=\frac{\left(\begin{array}{cc}7& -5\\ 2& 1\end{array}\right)}{17}$
if
$\left(\begin{array}{cc}1& 5\\ -2& 7\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}-10\\ -31\end{array}\right)⇒=\left(\begin{array}{cc}\frac{7}{17}& \frac{-5}{17}\\ \frac{2}{17}& \frac{1}{17}\end{array}\right)\left(\begin{array}{c}-10\\ -31\end{array}\right)$
$⇒\left(\begin{array}{c}-\frac{70}{17}+\frac{155}{17}\\ -\frac{20}{17}-\frac{31}{17}\end{array}\right)$
$⇒\left(\begin{array}{c}\frac{85}{17}\\ \frac{-51}{17}\end{array}\right)=\left(\begin{array}{c}5\\ -3\end{array}\right)$