Graphing Inequalities/Systems of Inequalities in Two Variables

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

How do you graph a linear inequality in two variables?

Back

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

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all ordered pairs (x, y) that make the inequality true.

Front

What is a system of inequalities?

Back

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

Front

How do you find the solution to a system of inequalities?

Back

To find the solution to a system of inequalities, graph each inequality on the same coordinate plane and identify the region where the shaded areas overlap.

Front

What does it mean for a point to be a solution to an inequality?

Back

A point is a solution to an inequality if it makes the inequality true when substituted into the inequality.

Front

What is the significance of the boundary line in graphing inequalities?

Back

The boundary line indicates the limit of the solution set. Points on the line may or may not be included in the solution set, depending on whether the inequality is strict (< or >) or inclusive (≤ or ≥).

Front

How can you determine if a point is a solution to an inequality?

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality and check if the statement is true.