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

1. Graph the corresponding linear equation as a boundary line. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the region that satisfies the inequality.

Front

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

Back

Shading above a line indicates that the solutions to the inequality are all the points above that line, meaning the y-values are greater than the values on the line.

Front

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

Back

Shading below a line indicates that the solutions to the inequality are all the points below that line, meaning the y-values are less than the values on the line.

Front

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

Back

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

Front

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

Back

Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is part of the solution set.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the set of all points that satisfy all inequalities in the system, often represented as a shaded region on a graph.

Front

What does the inequality symbol '≥' indicate?

Back

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

Front

What does the inequality symbol '≤' indicate?

Back

The symbol '≤' indicates that the value on the left is less than or equal to the value on the right.

Front

How do you write an inequality from a graph?

Back

Identify the slope and y-intercept of the boundary line, determine if the line is solid or dashed, and decide whether to shade above or below the line based on the direction of the inequality.