Solving 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

What does a dotted line represent when graphing inequalities?

Back

A dotted line represents that the points on the line are not included in the solution set, used for inequalities with < or >.

Front

What does a solid line represent when graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set, used for inequalities with ≤ or ≥.

Front

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

Back

Substitute the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the graphical representation of the inequality y > 2?

Back

The area above the line y = 2, with a dotted line indicating that points on the line are not included.

Front

What is the graphical representation of the inequality y ≤ x - 3?

Back

The area below the line y = x - 3, with a solid line indicating that points on the line are included.

Front

What does the inequality x ≤ -2 represent on a number line?

Back

All points to the left of -2, including -2 itself.

Front

How do you graph the system of inequalities y ≥ -2 and y ≤ x - 3?

Back

Graph the line y = -2 as a solid line and the line y = x - 3 as a solid line, then shade the area above y = -2 and below y = x - 3.

Front

What is the solution set of the system of inequalities y > 2 and y < 4?

Back

The region between the lines y = 2 and y = 4, not including the lines themselves.

Front

What is the significance of the intersection of two inequality graphs?

Back

The intersection represents the set of all points that satisfy both inequalities.