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 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 does the boundary line represent in a graph of inequalities?

Back

The boundary line represents the points where the inequality changes from true to false. It is included in the solution if the inequality is 'less than or equal to' or 'greater than or equal to'.

Front

What is the difference between 'less than' and 'less than or equal to'?

Back

'Less than' (<) does not include the boundary line, while 'less than or equal to' (≤) includes the boundary line in the solution set.

Front

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

Back

'>' indicates that the values on the left side of the inequality are greater than the values on the right side, excluding the boundary.

Front

How do you graph a system of inequalities?

Back

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

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.

Front

How can you check if an ordered pair is a solution to a system of inequalities?

Back

Substitute the x and y values of the ordered pair into each inequality. If both inequalities are satisfied, the ordered pair is a solution.

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, it is included in the solution set if the inequality is '≤' or '≥', but not if it is '<' or '>'.

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 will be shaded.