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.

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

Short answer

The given system is inconsistent.

Step-by-step solution

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.

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

The statement formed is false.

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