You are solving the equations
[tex]x= \begin{bmatrix}11 \\ 7\end{bmatrix}= a\begin{bmatrix}1 \\ 2\end{bmatrix}+ b\begin{bmatrix}3 \\ 1\end{bmatrix}[/tex]
which is the same as the two equations a+ 3b= 11 and 2a+ b= 7. Can you solve for a and b?
And
[tex]y= \begin{bmatrix}-5 \\ 5\end{bmatrix}= c\begin{bmatrix}1 \\ 2\end{bmatrix}+ d\begin{bmatrix}3 \\ 1\end{bmatrix}[/tex]
which is the same as the two equations c+ 3d= -5 and 2c+ d= 5. Can you solve for a and b?