Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

What does the symbol '≤' represent in an inequality?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

What does the symbol '≥' represent in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left can be greater than or equal to the value on the right.

Front

When graphing the inequality y < 2x + 3, what type of line is used?

Back

A dashed line is used when graphing y < 2x + 3 because the inequality does not include equality.

Front

When graphing the inequality y ≥ -x - 1, what type of line is used?

Back

A solid line is used when graphing y ≥ -x - 1 because the inequality includes equality.

Front

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

Back

A point is a solution if it satisfies all inequalities in the system, meaning it lies in the overlapping region of the graphs.

Front

What is the graphical representation of the inequality y < 3?

Back

The graphical representation is a horizontal line at y = 3, with a dashed line indicating that points on the line are not included.

Front

What is the solution set of the system of inequalities y ≤ 2x - 1 and y > -2x + 3?

Back

The solution set is the region where the area below the line y = 2x - 1 overlaps with the area above the line y = -2x + 3.

Front

What does it mean to 'solve a system of inequalities by graphing'?

Back

It means to graph each inequality on the same coordinate plane and identify the region where the solutions overlap.

Front

What is the significance of the shaded region in the graph of a system of inequalities?

Back

The shaded region represents all the possible solutions that satisfy all inequalities in the system.