Question

1. which statement describes the solution set of the system of linear inequalities graphed below? view image description the system has no solution. the solution set is only the shaded region above the dashed line. the solution set is only the shaded region below the solid line. the system has an infinite number of solutions.

Explanation:

Step1: Analyze the Graph

The graph shows two linear inequalities: one with a dashed line (indicating \(<\) or \(>\)) and one with a solid line (indicating \(\leq\) or \(\geq\)). The region between them is white (the overlapping solution region), and the surrounding is purple. But for a system of linear inequalities, the solution set is the intersection of the solution regions of each inequality. However, here we look at the options.

Step2: Evaluate Each Option

• Option 1: "No solution" is wrong because there's a white region (overlap) which is the solution.
• Option 2: "Only above dashed line" is wrong as the solid line also has a region, and the solution is the overlap (white), not just above dashed.
• Option 3: "Only below solid line" is wrong for similar reasons.
• Option 4: The white region (overlap) is infinite because it's a region between two parallel lines (since the lines have the same slope, they are parallel) extending infinitely, so there are infinitely many points in that region. So the system has infinite solutions.

Answer:

The system has an infinite number of solutions.