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

What does it mean for a point to be part of the solution set of a system of inequalities?

Back

A point is part of the solution set if it satisfies all inequalities in the system.

Front

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

Back

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

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

What does the inequality y ≥ -x - 1 represent graphically?

Back

It represents the region above and including the line y = -x - 1.

Front

What does the inequality y < x + 4 represent graphically?

Back

It represents the region below the line y = x + 4, not including the line itself.

Front

What is the significance of the solution set in a system of inequalities?

Back

The solution set represents all possible solutions that satisfy all inequalities in the system.

Front

Can a system of inequalities have no solution?

Back

Yes, if the inequalities represent parallel lines that do not intersect, there is no solution.

Front

What does it mean if a system of inequalities has an infinite number of solutions?

Back

It means that there are countless points that satisfy all inequalities, often occurring when the inequalities overlap significantly.

Front

How do you graph a system of inequalities?

Back

Graph each inequality on the same coordinate plane, shading the appropriate regions that satisfy each inequality.