Chapter EP, Problem 3.1.11EP

To determine

Graph each system of equations and describe it as consistent and independent, consistent or dependent, or inconsistent.

Answer to Problem 3.1.11EP

The graph created by system of equation $\frac{3}{4}x-y=0$ and $\frac{1}{3}y+\frac{1}{2}x=6$ is “Consistent and Independent”.

Explanation of Solution

Given information:

The given equations are:

  $\begin{array}{l}\frac{3}{4}x-y=0\\ \frac{1}{3}y+\frac{1}{2}x=6\end{array}$

Now let us plot graph for the equations $\frac{3}{4}x-y=0$ and $\frac{1}{3}y+\frac{1}{2}x=6$ to describe the relation between them:

As we can see from the above graph that both the equation $\frac{3}{4}x-y=0$ and $\frac{1}{3}y+\frac{1}{2}x=6$ is plotting lines which are intersecting each other only once, so there is one solution and the lines are “Consistent and Independent”.