## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Cramer's rule states that $a x+b y=p \\ cx+dy=q$ $\triangle=\left|\begin{array}{ll}{a}&{b}\\{c}&{d}\end{array}\right|, \triangle_{1}=\left|\begin{array}{ll}{p}&{b}\\{q}&{d}\end{array}\right|, \triangle_{2}=\left|\begin{array}{ll}{a}&{p}\\{c}&{q}\end{array}\right|$; $x=\dfrac{\triangle_1}{\triangle}; y=\dfrac{\triangle_2}{\triangle} (D\displaystyle \neq 0)$ From the given system of equations, we have: $\left[\begin{array}{ll}a & b\\c & d \end{array}\right]=\left[\begin{array}{ll} -1 & 2\\ 4 & -8 \end{array}\right]$ and $\left[\begin{array}{l} p\\q \end{array}\right]=\left[\begin{array}{l} 5\\6\end{array}\right]$ But $\triangle = \left|\begin{array}{ll} -1 & 2\\ 4 & -8 \end{array}\right|=8-8=0$ We see that determinant of the given system is $0$. So, we cannot apply Cramer's rule to find the values of $x$ and $y$.