Question

solving systems of linear inequalities quiz

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

Explanation:

Identify the target point

Using the Graphical Solution of Systems knowledge point
We need to determine if the point \((-3, 0)\) lies within the shaded solution region of the system of linear inequalities shown on the graph.

Locate the point on the coordinate plane

Using the Linear Inequalities knowledge point
Find the coordinates on the grid:

• Start at the origin \((0,0)\).
• Move \(3\) units to the left along the horizontal \(x\)-axis to reach \(x = -3\).
• Since the \(y\)-coordinate is \(0\), do not move vertically.
• The point \((-3, 0)\) lies directly on the \(x\)-axis at \(x = -3\).

Check if the point is in the shaded region

Using the Graphical Solution of Systems knowledge point

• Look at the shaded region (the red-shaded area in the lower-left quadrant).
• The shaded region represents the set of all points that satisfy both inequalities simultaneously.
• At \(x = -3\) on the \(x\)-axis, the region is shaded. Specifically, the shaded region extends upwards to the solid boundary line, which crosses the \(x\)-axis at \(x = -2\).
• Since \(-3 < -2\), the point \((-3, 0)\) lies completely inside the shaded region.
• Therefore, the statement "The point \((-3, 0)\) is in the solution set" is true.

Answer:

• True (Correct answer)
• False