System 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

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the region that satisfies the inequality.

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 inequalities in the system, meaning it lies in the shaded region of the graph.

Front

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

Back

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

Front

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

Back

To determine if a point is a solution, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the graphical representation of the inequality y > 2x - 4?

Back

The graphical representation is a dashed line for y = 2x - 4, with the region above the line shaded.

Front

What does the inequality y ≤ 2x - 1 represent graphically?

Back

It represents a solid line for y = 2x - 1, with the region below the line shaded.

Front

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

Back

The solution set is the region where the area below the line y = 2 and above the line y = -2x + 3 overlap.

Front

How do you identify a point that is not a solution to a system of inequalities?

Back

A point that does not satisfy at least one of the inequalities in the system is not a solution.

Front

What is the significance of the intersection of shaded regions in a system of inequalities?

Back

The intersection of shaded regions represents the set of all solutions that satisfy all inequalities in the system.