## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$x=2, y=-1 \text{ or } (2,-1)$
We will write the system $\left\{\begin{array}{r}{6x+5y=7}\\{2x+2y=2}\end{array}\right.$ in matrix form as: $AX=B$ where, $X=\left[\begin{array}{l}x\\y \end{array}\right]$ We have: $A=\left[\begin{array}{ll}{6}&{5}\\{2}&{2}\end{array}\right]$, and its inverse is: $A^{-1}=\left[\begin{array}{rr}{1}&{-5/2}\\{-1}&{3}\end{array}\right]$ Thus, the solution of the given matrix can be expressed as: $X=A^{-1}B=\left[\begin{array}{rr}{1}&{-5/2}\\{-1}&{3}\end{array}\right]\left[\begin{array}{l} 7\\2\end{array}\right]$ $\left[\begin{array}{l} x\\y \end{array}\right]=\left[\begin{array}{l} 7-5\\ -7+6 \end{array}\right]=\left[\begin{array}{l} 2\\-1\end{array}\right]$ So, our solution is:(2,-1)\$