# Solve the system of equations; x - 2y = 2 and 3x - 5y = 9 by writing and solving a matrix equation. Show all your work.

y=[latex] \frac{28}{11} [/latex] x=[latex] \frac{3}{11} [/latex] Working; Start by forming a matrix as shown below; [latex] \left[\begin{array}{ccc}1&-2\\3&5\end{array}\right] ( \left[\begin{array}{ccc}x\\y\end{array}\right])= ( \left[\begin{array}{ccc}2\\9\end{array}\right])[/latex] Step II Finding the inverse of the matrix as shown below; Determinant; (1*5)-(3*(-2)=11 Inverse; [latex] \frac{1}{11} \left[\begin{array}{ccc}5&2\\-3&1\end{array}\right] \left[\begin{array}{ccc}1&-2\\3&5\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right]= \frac{1}{11} \left[\begin{array}{ccc}5&2\\-3&1\end{array}\right] \left[\begin{array}{ccc}2\\9\end{array}\right][/latex] Evaluating further; [latex] \frac{1}{11} \left[\begin{array}{ccc}11&0\\0&11\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \frac{1}{11} \left[\begin{array}{ccc}28\\3\end{array}\right] [/latex] x=[latex] \frac{28}{11} and y = \frac{3}{11}[/latex]