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 region where the graphs of the inequalities overlap.

Front

How do you graph a linear inequality?

Back

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

Front

What does it mean to shade above or below a line in a graph?

Back

Shading above a line indicates that the solutions are greater than the line (y > mx + b), while shading below indicates that the solutions are less than the line (y < mx + b).

Front

What is the significance of the boundary line in a system of inequalities?

Back

The boundary line represents the values where the inequality changes from true to false. Solutions to the inequality are found in the shaded region.

Front

How do you determine which side of the line to shade for the inequality y < mx + b?

Back

Choose a test point not on the line (commonly (0,0)). If the point satisfies the inequality, shade the side of the line that includes the test point.

Front

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

Back

The symbol '≥' indicates that the value is greater than or equal to the number, meaning the boundary line is included in the solution.

Front

What does the symbol '<' indicate in an inequality?

Back

The symbol '<' indicates that the value is less than the number, meaning the boundary line is not included in the solution.

Front

How can you write an inequality from a graph?

Back

To write an inequality from a graph, identify the slope and y-intercept of the line, determine if the line is solid or dashed, and decide whether to use < or > based on the shading.

Front

What is the solution to the system of inequalities?

Back

The solution to a system of inequalities is the set of all points that satisfy all inequalities in the system, represented by the overlapping shaded regions.

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 >).