A.3H 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 the symbol '≤' mean 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 '≥' mean 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 - 1, what type of line is used?

Back

A solid line is used when graphing y ≤ 2x - 1 because the inequality includes 'equal to'.

Front

What type of line is used for the inequality y < -2x + 3?

Back

A dashed line is used for y < -2x + 3 because the inequality does not include 'equal to'.

Front

How do you determine the solution set for a system of inequalities?

Back

The solution set is determined by finding the region where the shaded areas of all inequalities overlap on the graph.

Front

What is the graphical representation of the inequality y > 3x?

Back

The area above the line y = 3x is shaded, and a dashed line is used to indicate that points on the line are not included.

Front

What does it mean if a point (x, y) satisfies the system of inequalities?

Back

It means that the point lies in the overlapping shaded region of the graph for all inequalities in the system.

Front

How do you solve a system of inequalities by graphing?

Back

1. Graph each inequality on the same coordinate plane. 2. Shade the appropriate region for each inequality. 3. Identify the overlapping shaded region as the solution.

Front

What is the solution to the system of inequalities y ≤ 3x and y > -2x + 4?

Back

The solution is the region where y is less than or equal to 3x and greater than -2x + 4, which is the overlapping area.