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 a solid line represent in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set, meaning the inequality is 'greater than or equal to' (≥) or 'less than or equal to' (≤).

Front

What does a dashed line represent in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set, meaning the inequality is 'greater than' (>) or 'less than' (<).

Front

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

Back

1. Graph the line y = 2x + 3 with a dashed line. 2. Shade below the line to represent all points where y is less than 2x + 3.

Front

What is the solution to the system of inequalities: y ≥ -x - 1 and y < x + 4?

Back

The solution is the region where the shaded areas of both inequalities overlap on the graph.

Front

What does the inequality x > -3 represent on a number line?

Back

It represents all numbers to the right of -3, not including -3 itself.

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 a solution.

Front

What is the graphical representation of the inequality y ≥ 3?

Back

A horizontal solid line at y = 3, with shading above the line.

Front

What is the difference between 'y < mx + b' and 'y ≤ mx + b'?

Back

'y < mx + b' uses a dashed line, while 'y ≤ mx + b' uses a solid line, indicating that the line itself is included in the solution.

Front

How do you solve a system of inequalities by graphing?

Back

1. Graph each inequality on the same coordinate plane. 2. Identify the overlapping shaded region, which represents the solution.