Linear Inequalities & Systems of Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is an inequality that involves a linear function, typically expressed in the form ax + by < c, ax + by > c, ax + by ≤ c, or ax + by ≥ c.

Front

How do you represent a solution to a system of linear inequalities graphically?

Back

A solution to a system of linear inequalities is represented graphically by the region where the shaded areas of the inequalities overlap.

Front

What does the symbol '>' indicate in a linear inequality?

Back

The symbol '>' indicates that the values of the variable are greater than the value on the other side of the inequality.

Front

What does the symbol '≥' indicate in a linear inequality?

Back

The symbol '≥' indicates that the values of the variable are greater than or equal to the value on the other side of the inequality.

Front

What type of line is used to represent '>' or '<' in a graph of a linear inequality?

Back

A dotted line is used to represent '>' or '<' in a graph of a linear inequality.

Front

What type of line is used to represent '≥' or '≤' in a graph of a linear inequality?

Back

A solid line is used to represent '≥' or '≤' in a graph of a linear inequality.

Front

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

Back

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

Front

What is the graphical representation of the inequality y < 2?

Back

The graphical representation of the inequality y < 2 is a solid horizontal line at y = 2, with the area below the line shaded.

Front

What is the significance of the intersection of two linear inequalities?

Back

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

Front

What does the inequality y ≥ x + 4 represent graphically?

Back

The inequality y ≥ x + 4 represents the region above and including the line y = x + 4.