Q. 23 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 15 – 42, solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so. 

$\left\{\begin{array}{l}3x-2y=4\\ 6x-4y=0\end{array}\right.$

Step-by-Step Solution

Answer

For the given system of equations Cramer's rule is not applicable because $D=0.$

Step 1. Given Information

The given system of equation is

$\left\{\begin{array}{l}3x-2y=4\\ 6x-4y=0\end{array}\right.$

We have to solve the system of equations using Cramer's rule if it is applicable.

Step 2. Finding the determinant

The determinant D of the coefficients of the variables is

$$\begin{gathered} D=\left|\begin{array}{cc}3& -2\\ 6& -4\end{array}\right| \\ D=\left(3\right)\left(-4\right)-\left(-2\right)\left(6\right) \\ D=\left(-12\right)-\left(-12\right) \\ D=0 \end{gathered}$$

Since $D=0$ Cramer's rule is not applicable.