Math Problem Statement

Solve the system of two linear inequalities graphically. x > 4 or y ≥ 2. Select and graph the option that describes the overall solution set.

Solution

The system you've provided involves solving two linear inequalities graphically:

  1. x>4x > 4
  2. y2y \geq 2

Steps for Solving Graphically:

  • Inequality 1: x>4x > 4 This represents a vertical line at x=4x = 4. The region where x>4x > 4 is to the right of this line.

  • Inequality 2: y2y \geq 2 This represents a horizontal line at y=2y = 2. The region where y2y \geq 2 is above this line.

The Overall Solution Set:

  • The solution to this system is the intersection of these two regions: the area to the right of x=4x = 4 and above y=2y = 2. The intersection is the region where both conditions are satisfied simultaneously, meaning the area in the upper-right section of the graph (above the line y=2y = 2 and to the right of x=4x = 4).

Correct Answer:

You should select "the intersection of the individual solution sets" for shading.

Would you like further details or help with another part of this problem?

Here are 5 related questions you might find interesting:

  1. How can we solve a system of linear inequalities involving different types of lines, such as vertical and horizontal?
  2. How do you graph an inequality like y<3x+1y < 3x + 1 on a coordinate plane?
  3. What is the difference between a system of equations and a system of inequalities graphically?
  4. How do you shade regions for inequalities in a multi-variable system?
  5. Can you explain how to solve inequalities involving quadratic functions graphically?

Tip: When graphing inequalities, always first plot the boundary line (or curve), then determine which side of the boundary should be shaded based on the inequality sign.

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Math Problem Analysis

Mathematical Concepts

Linear Inequalities
Graphical Solution
Coordinate Geometry

Formulas

Boundary Line Equations: x = 4, y = 2

Theorems

Properties of Inequalities
Intersection and Union of Solution Sets

Suitable Grade Level

Grades 9-12