i first convert the bases into a 2x2 matrix and then i multiplied the inverse matrix by the 2x1 e/f matrix of 9 (on top) and -8 (on the bottom)
which gave me x = 5.4 and y = 5 however the answer sheets states that x= 2 and y=5
May i please have some help on where I'm going wrong? Am i not multiplying the signs correctly? thank you for your help.
Hint:
In matrix notation we have: $$ Ax=b $$ with $$ A=\begin{bmatrix} 2&1\\1&-2 \end{bmatrix} \qquad x=\begin{bmatrix} x\\y \end{bmatrix}\qquad b=\begin{bmatrix} 9\\-8 \end{bmatrix} $$ so $$x=A^{-1}b$$ with $$ A^{-1}=\frac{1}{5}\begin{bmatrix} 2&1\\1&-2 \end{bmatrix} $$