System of Inequalities

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Definition of System of Inequalities

A System of Equations is a set of two or more equations with the same variables graphed on the same coordinate plane.

Examples of System of Inequalities

    The figure below shows the graph of the system of inequalities
    2x - 6y < 12, 3x + 4y < 12, and 4x + 2y ≥ 8.

Video Examples: Algebra 2- Solving Systems of Equations


Solved Example on System of Inequalities

Ques: Which of the graphs defines the system of inequalities, x + y < 3, - 5x + 2y ≤ 10, y ≥ - 3?.

    Choices:
    A. Graph-1
    B. Graph-2
    C. Graph-3
    D. Graph-4
    Correct Answer: A

Solution:

    Step 1: Graph all the three inequalities in the same coordinate plane.
    Step 2: The graph of x + y < 3 is the half-plane below the dashed line x + y = 3.
    Step 3: The graph of - 5x + 2y ≤ 10 is the half-plane on and below the solid line - 5x + 2y = 10.
    Step 4: The graph of y ≥ - 3 is the half-plane on and above the solid line y = - 3.
    Step 5: The graph of the system is the intersection of the three half planes as shown in the graph.
    Step 6: Graph-1 is the correct answer.

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