y=[tex] \frac{28}{11} [/tex]
x=[tex] \frac{3}{11} [/tex]
Working;
Start by forming a matrix as shown below;
[tex] \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])[/tex]
Step II
Finding the inverse of the matrix as shown below;
Determinant;
(1*5)-(3*(-2)=11
Inverse;
[tex] \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][/tex]
Evaluating further;
[tex] \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] [/tex]
x=[tex] \frac{28}{11} and y = \frac{3}{11}[/tex]
