System of Inequalities
A number a > a number b if a - b is positive.
i.e. a > b
Example: 2 > 1 because 2-1 = 1 is positive.
-1 > 2 is false because -1-2 = -3 is negative.
Rules for inequalities:
Definition of System of Inequalities
Examples of System of Inequalities
The figure below shows the graph of the system of inequality y ≤ x+2
The figure below shows the graph of the system of inequalities 2x - 6y < 12, 3x + 4y < 12, and 4x + 2y ≥ 8.
Choose the correct graph:
Which of the graphs defines the system of inequalities, x + y < 3, - 5x + 2y ≤ 10, y ≥ - 3?
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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