Question

Given the system of equations, what is the value of the system determinant? x + y = 8 x - y = 10

Answer 1

Two equations in the system:
1 x + 1 y = 8
1 x - 1 y = 10

Matrix notation:
\[\left[\begin{matrix}1 & 1 \\ 1 & -1\end{matrix} | \begin{matrix}8 \\ 10\end{matrix} \right]\]

The system determinant takes the coefficients A to the left (the x,y values)
and calculates a value for this square matrix.
\[\left| \left[\begin{matrix}a & b \\ d & e\end{matrix}\right] \right| = ae - bd\]