Systems of Linear Inequalities

Front

What is a system of linear inequalities?

Back

A set of two or more linear inequalities involving the same variables.

Front

What does it mean for a point to be a solution to a system of linear inequalities?

Back

A point is a solution 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 point's coordinates into each inequality; if all inequalities are true, it is a solution.

Front

What is the graphical representation of a linear inequality?

Back

It is represented by a line and a shaded region indicating the solution set.

Front

What type of line is used for inequalities with < or >?

Back

A dashed line is used.

Front

What type of line is used for inequalities with ≤ or ≥?

Back

A solid line is used.

Front

What does the shading in a graph of an inequality represent?

Back

The shading indicates the set of all solutions that satisfy the inequality.

Front

How do you graph the inequality y ≤ 2x + 3?

Back

Graph the line y = 2x + 3 as a solid line and shade below it.

Front

What is the solution set of the system y > 3x and y < -2x + 4?

Back

The area where the two shaded regions overlap, which is on the left side of the graph.

Front

What is the significance of the point (0,0) in a system of inequalities?

Back

It is often tested to see if it is a solution; if it satisfies all inequalities, it is a solution.