# Solve $3x+2y=9$ and $4x+5y=5$

let M=\begin{pmatrix}3&2\\4&5\end{pmatrix}
\det M=(3)(5)-(2)(4)=7
M^{-1}=\frac17\begin{pmatrix}5&-2\\-4&3\end{pmatrix}
\begin{pmatrix}x\\y\end{pmatrix}=\frac17\begin{pmatrix}5&-2\\-4&3\end{pmatrix}\begin{pmatrix}9\\5\end{pmatrix}=\frac17\begin{pmatrix}35\\-21\end{pmatrix}
\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}5\\-3\end{pmatrix}
x=5
y=-3

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