Q. 2 - Precalculus Enhanced with Graphing Utilities

Question

Using Cramer’s Rule, the value of x that satisfies the system of equations $\left\{\begin{array}{l}2x+3y=5\\ x-4y=-3\end{array}\right.$  is $x=\frac{}{\left|\begin{array}{cc}2& 3\\ 1& -4\end{array}\right|}$.

Step-by-Step Solution

Answer

$x=\frac{\left|\begin{array}{cc}5& 3\\ -3& -4\end{array}\right|}{\left|\begin{array}{cc}2& 3\\ 1& -4\end{array}\right|}$

Step 1. Given information

We have been given that the value of x that satisfies the system of equations $\left\{\begin{array}{l}2x+3y=5\\ x-4y=-3\end{array}\right.$ is $x=\frac{}{\left|\begin{array}{cc}2& 3\\ 1& -4\end{array}\right|}$.

We have to complete it. 

Step 2. Complete using the Cramer's rule

Using Cramer's rule, we can write x as:

$x=\frac{\left|\begin{array}{cc}5& 3\\ -3& -4\end{array}\right|}{\left|\begin{array}{cc}2& 3\\ 1& -4\end{array}\right|}$