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

What does it mean for a point to be part of the solution set of a system of inequalities?

Back

A point is part of the solution set if it satisfies all the inequalities in the system.

Front

How do you determine if a point is a solution to an inequality?

Back

To determine if a point is a solution, substitute the coordinates of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the difference between a solid line and a dashed line when 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 <).

Front

How do you graph the inequality y > 2?

Back

To graph y > 2, draw a dashed horizontal line at y = 2 and shade the area above the line.

Front

What does the inequality y ≤ 3 represent on a graph?

Back

The inequality y ≤ 3 represents all points on or below the horizontal line y = 3.

Front

How can you convert the inequality -y < x - 8 into slope-intercept form?

Back

To convert -y < x - 8, multiply by -1 (reversing the inequality) to get y > -x + 8.

Front

What is the solution to the inequality y - 4 > 12?

Back

The solution is y > 16.

Front

What does the inequality x ≥ 3 mean in terms of a graph?

Back

The inequality x ≥ 3 means all points to the right of and including the vertical line x = 3.

Front

How do you find the intersection of two inequalities?

Back

To find the intersection, graph both inequalities and identify the region where they overlap.