Question

question 9 of 10
select the points that are solutions to the system of inequalities. select all that apply.
text description for graph
a. (0, 0)
b. (-12, 0)
c. (-10, 1)
d. (1, 2)

Explanation:

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

Step 1: Analyze the graph’s boundaries

• The dashed line (sloped, positive) and solid line (sloped, negative) define the inequalities. The shaded region is the overlap of the solution sets for both inequalities.
• The shaded area appears to lie in the left - hand side (negative \( x \) - values, or \( x < 0 \) - like behavior, combined with specific \( y \) - value constraints) and within the intersection of the two inequality regions.

Step 2: Test each point

• Option A: \((0, 0)\)

The point \((0, 0)\) lies on the intersection of the axes. From the graph, the shaded region does not include the origin (visually, the shaded area is to the left of the intersection point of the two lines, and \((0,0)\) is on the boundary but not in the shaded overlap). So, \((0, 0)\) is not a solution.

• Option B: \((-12, 0)\)

The \( x \) - value \(-12\) is far to the left, outside the visible grid (the graph’s grid seems to range around \( x = - 10 \) to \( x = 10 \)). The shaded region is within a more restricted \( x \) - range (likely \( x \geq - 10 \) or similar, based on the graph’s scale). So, \((-12, 0)\) is not a solution.

• Option C: \((-10, 1)\)

The \( x \) - value \(-10\) is on the left boundary of the visible grid, and the \( y \) - value \( 1 \) is positive. Visually, this point lies within the shaded region (overlap of the two inequality solutions). So, \((-10, 1)\) is a solution.

• Option D: \((1, 2)\)

The \( x \) - value \( 1 \) is positive (right of the \( y \) - axis), but the shaded region is on the left - hand side (negative \( x \) - values or restricted left region). Thus, \((1, 2)\) is not in the shaded area and is not a solution.

Answer:

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