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

Front

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

Back

A point is a solution to a system of inequalities if it satisfies all the inequalities in the system, meaning it lies in the region defined by the inequalities when graphed.

Front

What is the difference between a solid line and a dashed line when graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set (used for ≤ or ≥), while a dashed line indicates that the points on the line are not included (used for < or >).

Front

How do you determine if a point is a solution to a linear inequality?

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a half-plane divided by a line, where one side of the line represents the solutions to the inequality.

Front

What does the symbol '>' mean in an inequality?

Back

The symbol '>' means 'greater than' and indicates that the value on the left side of the inequality is larger than the value on the right side.

Front

What does the symbol '<' mean in an inequality?

Back

The symbol '<' means 'less than' and indicates that the value on the left side of the inequality is smaller than the value on the right side.

Front

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

Back

To graph y < 2x + 3, first graph the line y = 2x + 3 with a dashed line, then shade the area below the line to represent all points where y is less than 2x + 3.

Front

What is the solution set of the system of inequalities y ≤ 2x + 1 and y > -x + 4?

Back

The solution set is the region where the area below the line y = 2x + 1 overlaps with the area above the line y = -x + 4.

Front

What does it mean for two inequalities to be consistent?

Back

Two inequalities are consistent if there is at least one solution that satisfies both inequalities simultaneously.