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 dashed line for < or > and a solid line for ≤ or ≥. The solution is the overlapping shaded region.

Front

What does the solution to a system of inequalities represent?

Back

The solution represents all the points (x, y) that satisfy all inequalities in the system.

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

Back

Substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the graphical representation of y < -x + 2?

Back

The graph is a dashed line with a y-intercept of 2 and a slope of -1, shaded below the line.

Front

What does the inequality y > 3 represent graphically?

Back

It represents a horizontal line at y = 3, with the area above the line shaded.

Front

How can you tell if a point lies in the solution region of a system of inequalities?

Back

By testing the point in the inequalities; if it satisfies all, it lies in the solution region.

Front

What is the significance of the intersection of shaded regions in a system of inequalities?

Back

The intersection represents the set of solutions that satisfy all inequalities in the system.

Front

What is the solution to the system: x + 2y ≥ 4 and 3x - 2y < 4?

Back

The solution includes points that satisfy both inequalities, such as (2, 2).