Question

1. arjun determines that a system of linear inequalities has an overlapping shaded region. which statement about the solutions is true? the system has infinite solutions. the system has one unique solution where the boundary lines intersect. there is not enough information to determine the number of solutions to the system. the system has no solution.

Explanation:

For a system of linear inequalities, the solution set is the region where all inequalities are satisfied. An overlapping shaded region means there are infinitely many points (solutions) within that intersection, as linear inequalities' solution regions are sets of points, not single points (unlike linear equations' intersection for a unique solution) and a non - empty overlap means solutions exist (so "no solution" is wrong) and we can determine there are infinite solutions (so "not enough info" is wrong), and the unique solution at intersection is for linear equations, not inequalities.

Answer:

A. The system has infinite solutions.