Systems of Inequalities

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all ordered pairs 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 dashed or solid line. Then, shade the region that satisfies the inequality (above for 'greater than', below for 'less than').

Front

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

Back

'≥' means 'greater than or equal to'. It indicates that the value can be either greater than or equal to the number.

Front

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

Back

'≤' means 'less than or equal to'. It indicates that the value can be either less than or equal to the number.

Front

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

Back

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

Front

How do you determine the solution set of a system of inequalities?

Back

The solution set is the region where the shaded areas of all inequalities overlap on the graph.

Front

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

Back

The graphical representation is a dashed horizontal line at y = 2, with the area above the line shaded.

Front

What is the graphical representation of the inequality y ≤ -x + 3?

Back

The graphical representation is a solid line with a slope of -1 and a y-intercept of 3, with the area below the line shaded.

Front

How do you solve a system of inequalities by graphing?

Back

1. Graph each inequality on the same coordinate plane. 2. Identify the overlapping shaded region. 3. This region represents the solution set.

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

If a point lies on the boundary line of an inequality, it is included in the solution set if the inequality is '≥' or '≤', but not included if the inequality is '>' or '<'.