College Algebra, Chapter 7, 7.4, Section 7.4, Problem 38

Solve the system $\left\{\begin{equation}
\begin{aligned}

10x - 17y =& 21
\\
20x - 31y =& 39

\end{aligned}
\end{equation} \right.$ using Cramer's Rule.

For this system we have


$
\begin{equation}
\begin{aligned}

|D| =& \left| \begin{array}{cc}
10 & - 17 \\
20 & - 31
\end{array} \right| = 10 \cdot (-31) - (-17) \cdot 20 = 30
\\
\\
|D_{x}| =& \left| \begin{array}{cc}
21 & -17 \\
39 & -31
\end{array} \right| = 21 \cdot (-31) - (-17) \cdot 39 = 12
\\
\\
|D_{y}| =& \left| \begin{array}{cc}
10 & 21 \\
20 & 39
\end{array} \right| = 10 \cdot 39 - 21 \cdot 20 = -30

\end{aligned}
\end{equation}
$


The solution is


$
\begin{equation}
\begin{aligned}

x =& \frac{|D_x|}{|D|} = \frac{12}{30} = \frac{2}{5}
\\
\\
y =& \frac{|D_y|}{|D|} = \frac{-30}{30} = -1

\end{aligned}
\end{equation}
$