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 < mx + b?

Back

Shade below the line for y < mx + b, as it represents all the points where y is less than the value of mx + b.

Front

What does a dashed line indicate in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set (i.e., the inequality is strict, such as < or >).

Front

What does a solid line indicate in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set (i.e., the inequality is non-strict, such as ≤ or ≥).

Front

How can you test 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 solution to a system of inequalities?

Back

The solution is represented by the shaded region where the graphs of the inequalities overlap.

Front

What is the significance of the boundary line in a system of inequalities?

Back

The boundary line separates the solution region from the non-solution region and indicates where the inequality changes from true to false.

Front

How do you graph the inequality y ≥ 2x - 3?

Back

Graph the line y = 2x - 3 with a solid line and shade above the line to represent all points where y is greater than or equal to 2x - 3.

Front

What is the difference between a strict and non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary, while a non-strict inequality (≤ or ≥) includes the boundary.

Front

Which of the following points is a solution to the inequality y < 2x + 1? (0, 0), (1, 3), (2, 5)

Back

(0, 0) is a solution because it satisfies the inequality; (1, 3) and (2, 5) do not.