What product represents the solution to the system?

Question

What product represents the solution to the system? $$-y+7x=14$$ $$-x+4y=1$$ I have that $y=\cfrac{7}{9}$ $x=\cfrac{19}{9}$

But how to place this as a setup of a product of two matrices?

Answer 1

You can rewrite the system as

$$\begin{bmatrix} 7 & -1 \\ -1 &4 \end{bmatrix}\begin{bmatrix} x \\ y\end{bmatrix}=\begin{bmatrix} 14 \\ 1\end{bmatrix}$$

You can try to use a matrix method to solve the system again.

Answer 2

$${7\ \ -1 \choose -1\ \ 4}{x \choose y} = {14 \choose 1}$$

Answer 3

\begin{align} \left[ \begin{matrix} 7 & -1\\ -1 & 4 \end{matrix} \right] \left[ \begin{matrix} x\\ y \end{matrix} \right] =\left[ \begin{matrix} 14 \\ 1 \end{matrix} \right]. \end{align} Then, \begin{align} \left[ \begin{matrix} x\\ y \end{matrix} \right] =&\left[ \begin{matrix} 7 & -1\\ -1 & 4 \end{matrix} \right]^{-1}\left[ \begin{matrix} 14 \\ 1 \end{matrix} \right]\notag\\ =&\left[ \begin{matrix} \frac{19}{9} \\ \frac{7}{9} \end{matrix} \right]. \end{align}