Question

Using the inverse of a matrix solve the following system of equation. Give your answer as an ordered pair.

Answer 1

We will have the following:

$A=\mleft(\begin{array}{cc}3 & 7 \\ -1 & -1 \\ \end{array}\mright)\Rightarrow A^{-1}=\mleft(\begin{array}{cc}-\frac{1}{4} & -\frac{7}{4} \\ \frac{1}{4} & \frac{3}{4} \\ \end{array}\mright)$$\Rightarrow X=(A^{-1})B\Rightarrow X=\mleft(\begin{array}{cc}-\frac{1}{4} & -\frac{7}{4} \\ \frac{1}{4} & \frac{3}{4} \\ \end{array}\mright)\mleft(\begin{array}{c}-4 \\ 2 \\ \end{array}\mright)$$\Rightarrow X=\mleft(\begin{array}{c}-\frac{5}{2} \\ \frac{1}{2} \\ \end{array}\mright)$