Systems of Inequalities

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

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How do you determine if a point is a solution to a system of inequalities?

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To determine if a point is a solution, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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What does it mean if a point is above the line in a graph of an inequality?

Back

If a point is above the line in a graph of an inequality, it means that the point satisfies the inequality, indicating that it is a solution.

Front

What does it mean if a point is below the line in a graph of an inequality?

Back

If a point is below the line in a graph of an inequality, it means that the point does not satisfy the inequality, indicating that it is not a solution.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution (≤ or ≥), while a dashed line indicates that the points on the line are not included ( < or >).

Front

How do you graph the inequality y > -2x + 1?

Back

1. Graph the line y = -2x + 1 with a dashed line. 2. Shade the area above the line to represent all points where y is greater than -2x + 1.

Front

How do you graph the inequality y ≤ x + 3?

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1. Graph the line y = x + 3 with a solid line. 2. Shade the area below the line to represent all points where y is less than or equal to x + 3.

Front

What is the solution region for a system of inequalities?

Back

The solution region is the area where the shaded regions of all inequalities overlap. This area contains all the points that satisfy all inequalities in the system.

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What does it mean if a point is a vertex of the solution region?

Back

A vertex of the solution region is a corner point where two or more boundary lines intersect. It is often a candidate for the optimal solution in linear programming.

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How can you find a solution to a system of inequalities?

Back

To find a solution, graph each inequality, identify the overlapping shaded region, and select any point within that region.