Find the ordered pair\((x,y)\) that satisfies the system of equations
\(\begin{align*} x+3y &= -4,\\ 3x -7y &= 36. \end{align*}\)
We can express the system in matrix form:
\(\begin{pmatrix} 1 & 3 \\ 3 & -7 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} -4 \\ 36 \end{pmatrix}\)
Inverting, we get x = 17/4 and y = -11/4, so the solution is (17/4, -11/4).
