Systems of Inequalities (SOI)

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

What does a solid line represent when graphing inequalities?

Back

A solid line represents that the points on the line are included in the solution set, which occurs when the inequality is ≤ or ≥.

Front

What does a dashed line represent when graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set, which occurs when the inequality is < 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 region on the graph where all inequalities overlap, representing all possible solutions.

Front

What is the graphical representation of the inequality y < 2x + 3?

Back

The graph will have a dashed line for y = 2x + 3, and the area below the line represents the solution set.

Front

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

Back

The boundary line separates the solution set from the non-solution set and helps visualize the inequalities.

Front

How do you graph the inequality 3x + 2y ≤ 6?

Back

First, graph the line 3x + 2y = 6 as a solid line, then shade below the line to represent the solution set.

Front

What is the difference between 'and' and 'or' in systems of inequalities?

Back

'And' means the solution must satisfy all inequalities simultaneously, while 'or' means the solution can satisfy at least one of the inequalities.

Front

What does the point (0, 0) represent in the context of a system of inequalities?

Back

(0, 0) is a specific point that can be tested to see if it satisfies the inequalities in the system.