Solving Systems of Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables.

Front

What does it mean for a system of inequalities to have an infinite number of solutions?

Back

It means that there are countless points that satisfy all inequalities in the system.

Front

What is the graphical representation of a linear inequality?

Back

A shaded region on one side of the boundary line, indicating all solutions.

Front

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

Back

Substitute the point into each inequality; if it satisfies all, it is a solution.

Front

What is the difference between '>' and '≥' in inequalities?

Back

'>' means not including the boundary line, while '≥' includes it.

Front

What does the solution set of a system of inequalities represent?

Back

The region on the graph where all inequalities overlap.

Front

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

Back

Draw the line y = 2x + 3 as dashed and shade below it.

Front

What is the significance of a dashed line in graphing inequalities?

Back

It indicates that points on the line are not included in the solution.

Front

What is the significance of a solid line in graphing inequalities?

Back

It indicates that points on the line are included in the solution.

Front

How can you solve a system of inequalities by graphing?

Back

Graph each inequality, then identify the overlapping shaded region.