System 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

How do you determine where to shade for the inequality y ≥ 3?

Back

Shade above the line y = 3, as it includes all points where y is greater than or equal to 3.

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 (for example, in y < x).

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 (for example, in y ≤ x).

Front

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

Back

First, graph the line y = -x + 2 with a dashed line, then shade below the line.

Front

What is the solution to the system of inequalities: y < 3 and y > -x + 2?

Back

The solution is the region where the area below the line y = 3 and above the line y = -x + 2 overlap.

Front

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

Back

It represents all numbers to the right of 2, not including 2 itself.

Front

How do you identify the boundary line for the inequality y ≤ 4?

Back

The boundary line is y = 4, which is a solid line because the inequality includes equal to (≤).

Front

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

Back

The line y = -2 is dashed, and the area above the line is shaded.

Front

How do you solve the system of inequalities: x < 2 and y < -4?

Back

Graph the line x = 2 (dashed) and y = -4 (dashed), then shade the area to the left of x = 2 and below y = -4.