Math Problem Statement

Solution

The image presents a math problem where you are asked to select the solution set for the system of inequalities from the graphed lines shown. The inequalities given are:

y &\leq \frac{1}{2}x + 2 \\ y &< \frac{3}{2}x - 5 \end{aligned}$$ The graph displays two lines, each corresponding to one of the inequalities. The solution set will be the region where both inequalities overlap on the graph. This region must satisfy both inequalities simultaneously. Let's analyze the solution choices: - **Option A (0, 10):** This point lies far above the y-intercept of the first inequality and the second line, so it's outside the solution region. - **Option B (2, 4):** This point appears to be within the region where both inequalities overlap. - **Option C (7, 7):** This point may lie on the boundary of the second inequality but doesn't satisfy the "less than" condition. - **Option D (3, 4):** Similar to Option B, this point is within the overlapping region. The correct answers should include only those points that lie within the region that satisfies both inequalities. The correct solution set appears to be **(2, 4) and (3, 4)**, as both points are within the region that satisfies both inequalities. ### Do you want more details or have any questions? Here are 5 related questions that expand on this topic: 1. How do you graph inequalities on a coordinate plane? 2. What is the significance of the boundary lines in the graph of a linear inequality? 3. How do you determine if a point satisfies a system of inequalities? 4. Can you explain how to find the intersection of two inequalities graphically? 5. What is the difference between "less than" and "less than or equal to" in graphing inequalities? **Tip:** Always check whether the boundary lines should be solid or dashed when graphing inequalities—this depends on whether the inequality includes equality (≤ or ≥) or is strict (< or >).

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Inequalities
Coordinate Geometry

Formulas

-

Theorems

-

Suitable Grade Level

Grades 9-12

Related Recommendation

Solving a System of Linear Inequalities: Graphing and Analysis

Graphing Systems of Inequalities and Finding Solution Sets

System of Linear Inequalities: Analyzing Feasible Regions

Solving Systems of Inequalities and Determining Feasible Regions

Solving Systems of Inequalities with Graphs - Example Questions 11 and 12