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 inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

What does it mean if a point is a solution to a system of linear inequalities?

Back

A point is a solution to a system of linear inequalities if it satisfies all the inequalities in the system, meaning it lies in the overlapping region of the graphs.

Front

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

Back

A solid line indicates that the points on the line are included in the solution (used for ≤ or ≥), while a dotted 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, the point is a solution.

Front

What is the graphical representation of the inequality y < 2x + 3?

Back

The graph of y < 2x + 3 will have a dotted line for y = 2x + 3, and the area below the line represents the solution set.

Front

What does the symbol '≥' indicate in an inequality?

Back

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

Front

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

Back

The symbol '<' indicates that the value on the left is less than the value on the right.

Front

How can you tell if an inequality will have a dotted line when graphed?

Back

An inequality will have a dotted line when it uses the symbols < or >, indicating that the boundary line is not included in the solution.

Front

What is the solution set of the inequality y ≥ 3?

Back

The solution set of y ≥ 3 includes all points on the line y = 3 and all points above this line.

Front

What is the significance of the intersection of two inequalities?

Back

The intersection of two inequalities represents the set of points that satisfy both inequalities simultaneously.