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 linear inequalities that share the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

What does the inequality x < -1 represent on a number line?

Back

It represents all numbers to the left of -1, not including -1 itself.

Front

How do you graph the inequality y < 3?

Back

You draw a horizontal dashed line at y = 3 and shade the area below the line.

Front

What does a dashed line indicate in the graph of an inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set.

Front

What does a solid line indicate in the graph of an inequality?

Back

A solid line indicates that the points on the line are included in the solution set.

Front

How can 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 solution set of the inequality y > 2x - 4?

Back

The solution set includes all points above the line y = 2x - 4, not including the line itself.

Front

What does the inequality y < 2x + 3 represent graphically?

Back

It represents all points below the line y = 2x + 3, with a dashed line indicating that points on the line are not included.

Front

Which of the following points is NOT a solution to the inequality y < 2x - 4? (0, 0), (0, 1), (-100, -3), (5, 10)

Back

(5, 10) is NOT a solution because it lies above the line y = 2x - 4.

Front

What is the significance of the shading in the graph of a linear inequality?

Back

The shading indicates the region of the graph that contains all the solutions to the inequality.