Solving 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 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 dashed or solid line. Then, shade the region that represents the solution set based on the inequality symbol (e.g., above the line for 'greater than' and 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 exactly 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 exactly equal to the number.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the region on the graph where the shaded areas of all inequalities overlap. It includes all points that satisfy all inequalities in the system.

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 difference between a dashed line and a solid line in graphing inequalities?

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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

What does it mean if a point lies outside the shaded region of a graph of inequalities?

Back

If a point lies outside the shaded region, it does not satisfy at least one of the inequalities in the system.

Front

How do you solve a system of inequalities by graphing?

Back

1. Graph each inequality on the same coordinate plane. 2. Use dashed or solid lines as appropriate. 3. Shade the solution regions for each inequality. 4. Identify the overlapping shaded region as the solution set.

Front

What is an example of a system of inequalities?

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Example: y > 2x + 1 and y ≤ -x + 4.