Chapter 6, Problem 1MCQ

To determine

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

Answer to Problem 1MCQ

The given equations are consistent, and their solution is independent

Explanation of Solution

Given information:

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

Formulaused:

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 isdependent,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 $y=2x-1$ and $y=-2x+3$ we see that the lines intersect at a point. That means they have only one solution that is point of intersections of these line.

Since, the given equations have solution so are consistent, and there is only one solution so the solution is independent.

Conclusion:

The given equations are consistent, and their solution is independent