Chapter 6, Problem 2MCQ

To determine

To find: The given system of equations is consistent or inconsistent and whether that is independent using given graph.

Answer to Problem 2MCQ

The given system of equations is inconsistent.

Explanation of Solution

Given information:

The given equations are $y=-2x+3$ , $y=-2x-3$ . The graph is shown in Figure-1 here.

Formula used:

If a system has at least one solution, then it is said to be consistent. If a consistent system of equations has exactly one solution, it is independent .

If a consistent system has an infinite number of solutions, it is dependent, when graphed such equations, represent the same line. If a system has no solution, it is said to be inconsistent .The graphs of such equations do not intersect, i.e., graphs are parallel.

From the graph of equations $y=-2x+3$ and $y=-2x-3$ we see that the lines are parallel so they do not intersect at a point. That means they do no have any solution, i.e. they are inconsistent.

Since, there is no solution so there is no category of the solutions being dependent or independent.

Conclusion:

The given system of equations is inconsistent.