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.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality on the same coordinate plane. Use a solid line for inequalities that include equality (≥ or ≤) and a dashed line for strict inequalities (> or <). Shade the region that satisfies each inequality.

Front

What does the solution set of a system of inequalities represent?

Back

The solution set represents all the points (x, y) that satisfy all inequalities in the system. It is the overlapping shaded region of the graphed inequalities.

Front

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

Back

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

Front

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

Back

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

Front

What does the inequality y ≥ 3 represent when graphed?

Back

The inequality y ≥ 3 represents all points on and above the horizontal line y = 3.

Front

Which of the following points is a solution to the system of inequalities: (4, 3), (0, 6), (-2, -5), (-8, 2)?

Back

(4, 3) is a solution to the system of inequalities.

Front

Which point is NOT part of the solution set for the system of inequalities: (0, 0), (5, 1), (-1, -3), (20, -5)?

Back

(-1, -3) is NOT part of the solution set.

Front

What does the inequality 5 ≥ x mean?

Back

The inequality 5 ≥ x means that x can take any value less than or equal to 5.

Front

How do you identify the boundary line of an inequality?

Back

The boundary line of an inequality is found by replacing the inequality sign with an equal sign and solving for y in terms of x.