Question

Use the graph at the right to determine whether each system is consistent or inconsistent and if it is independent or dependent.

$\begin{array}{c}\mathbf{y}\mathbf{=}\mathbf{2}\mathbf{x}\mathbf{+}\mathbf{3}\\ \mathbf{y}\mathbf{=}\mathbf{-}\mathbf{2}\mathbf{x}\mathbf{-}\mathbf{5}\end{array}$

Short answer

The given system of equations is consistent and independent.

Step-by-step solution

Step 1. Write the definition of consistent, inconsistent, dependent and independent system.

The system is said to be consistent if the system has one or more solutions.

The system is said to be inconsistent if the system has no solution.

The system is said to be independent if the system has one solution.

The system is said to be dependent if the system has more than one solution.

Step 2. Determine whether each system is consistent or inconsistent and if it is independent or dependent.

The given system of equations is:

$\begin{array}{l}y=2x+3\\ y=-2x-5\end{array}$

The given graph is:

From the given graph, it can be noticed that the lines$y=2x+3$and $y=-2x-5$are intersecting at only one point. Therefore, there is only one solution of the given system of equations.

As, the given system of equations has only one solution, therefore, the given system of equations is consistent and independent.