Question

select the points that are solutions to the system of inequalities. select all that apply.
text description for graph
a. (-10, 1)
b. (-12, 0)
c. (0, 0)
d. (1, 2)

Explanation:

To determine the solutions to the system of inequalities, we analyze the shaded region (solution region) from the graph:

Step 1: Analyze Point A \((-10, 1)\)

The point \((-10, 1)\) lies within the shaded region (as seen from the graph’s shaded area). Thus, it satisfies both inequalities.

Step 2: Analyze Point B \((-12, 0)\)

The graph’s boundary and shaded region do not extend to \(x = -12\) (the \(x\)-axis range in the graph is within \([-10, 10]\) for visibility, and \(-12\) is outside the graphed square’s \(x\)-boundary). Thus, \((-12, 0)\) is not in the solution region.

Step 3: Analyze Point C \((0, 0)\)

The origin \((0, 0)\) lies on the intersection of the two lines but outside the shaded region (the shaded area is to the left of the intersection, not at the origin). Thus, it does not satisfy the system.

Step 4: Analyze Point D \((1, 2)\)

The point \((1, 2)\) lies to the right of the shaded region (the shaded area is left of the intersection, and \((1, 2)\) is in the unshaded right region). Thus, it does not satisfy the system.

Answer:

A. \((-10, 1)\)