Question

the point (-3,0) is in the solution set.

true
false

Explanation:

Locate the point on the coordinate plane

Using the Ordered Pairs knowledge point
The given point is \((-3, 0)\). On the coordinate plane, this point lies on the horizontal \(x\)-axis, exactly \(3\) units to the left of the origin \((0,0)\).

Analyze the shaded solution region

Using the Systems of Linear Inequalities knowledge point
The solution set of the system of inequalities is represented by the overlapping shaded region (the dark red shaded area in the upper-left quadrant).
Let's check if the point \((-3, 0)\) lies within this shaded region:

• The point \((-3, 0)\) is on the \(x\)-axis.
• Looking at the graph, the shaded region is entirely above the solid boundary line in the region where \(x = -3\).
• At \(x = -3\), the solid boundary line is at \(y = 1\), and the shaded region is above this line (\(y \ge 1\)).
• Since the \(y\)-coordinate of our point is \(0\), which is below the shaded region, the point \((-3, 0)\) is outside the shaded solution set.

Determine the truth value

Since the point \((-3, 0)\) does not lie within the shaded region representing the solution set, the statement "The point \((-3,0)\) is in the solution set" is false.

Answer:

• True
• False (Correct answer)