Question

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

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

Short answer

The provided set of equation falls in the category of inconsistent.

Step-by-step solution

Step 1. State the definition of consistent and inconsistent along with this independent and dependent.

A system of equation falls in the category of consistent only when the count of the solutions associated with that system of equation is at least one. The solution associated with that system of the equation falls in the category of independent only when the count of the solution is one in count and the system of equation is consistent. The solution associated with that system of the equation falls in the category of dependent only when the count of the solution is not definite in count and the system of equation is consistent.

A system of equation falls in the category of inconsistent only when the count of the solutions associated with that system of equation is zero. This happens only when the graphs of the system of equation are having a parallel relation between them.

Step 2. Determine the count of the solutions associated with the provided set of equations.

The lines associated with the provided system of equations are not making any intersection so the count of solutions associated with this system is represented by 0.

Step 3. Write the conclusion.

The obtained count represents that the provided system of equation falls in the category of inconsistent.