Question

inequalities: practice

which solution is valid within the context of the situation?

(200.5, 50)
(180, 80)
(300, -40)
(100, 100)

Explanation:

🆕 New Concept Discovered: Solving Systems of Inequalities Graphically
Finding where shaded regions overlap on a coordinate plane

Step 1: Identify the solution region

A solution to a system of inequalities is represented by the region where the shaded areas of both inequalities overlap. On this graph, the solution set is the darker, doubly-shaded region in the middle.

Step 2: Evaluate the given options

We need to check which of the given coordinate points lies inside this darker overlapping region:

• \( (200.5, 50) \): Locate \( x \approx 200.5 \) and \( y = 50 \). This point lies clearly within the dark shaded band between the two boundary lines.
• \( (180, 80) \): Locate \( x = 180 \) and \( y = 80 \). This point lies above the boundary lines in the light blue region.
• \( (300, -40) \): Even though this point might fall in the region, in real-world contexts, negative values (like \( y = -40 \)) are typically invalid.
• \( (100, 100) \): Locate \( x = 100 \) and \( y = 100 \). This point lies below the dark shaded band in the light blue region.

Answer:

\( (200.5, 50) \)