Q. 5 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 1–10, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.   

$\left\{\begin{array}{l}x-3y+4=0\\ \frac{1}{2}x-\frac{3}{2}y+\frac{4}{3}=0\end{array}\right.$

Step-by-Step Solution

Answer

The given system is inconsistent.

Step 1. Given Information

We are given a system of equations $\left\{\begin{array}{l}x-3y+4=0\\ \frac{1}{2}x-\frac{3}{2}y+\frac{4}{3}=0\end{array}\right.$.

We need to solve the system of using the method of substitution or the method of elimination. 

Step 2. Use elimination method

Multiply the second equation by $2$.

$\begin{array}{rcl}2\left(\frac{1}{2}x-\frac{3}{2}y+\frac{4}{3}\right)& =& 2·0\\ x-3y+\frac{8}{3}& =& 0\end{array}$

Now subtract this equation from the first equation.

$\begin{array}{rcl}x-3y+4-(x-3y+\frac{8}{3})& =& 0-0\\ x-3y+4-x+3y-\frac{8}{3}& =& 0\\ 4-\frac{8}{3}& =& 0\\ \frac{4}{3}& =& 0\end{array}$

The statement formed is false.

So the given system has no solution and thus is inconsistent.