Systems of Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables. Solutions are the set of points that satisfy all inequalities in the system.

Front

How do you graph a linear inequality?

Back

1. Graph the boundary line (solid for ≥ or ≤, dashed for > or <). 2. Choose a test point to determine which side of the line to shade.

Front

What does the inequality y < -x - 1 represent graphically?

Back

It represents the region below the line y = -x - 1.

Front

What is the solution set of a system of inequalities?

Back

The set of all points that satisfy all inequalities in the system.

Front

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

Back

Substitute the point's coordinates into each inequality. If it satisfies all, it is a solution.

Front

What does shading above a line indicate in graphing inequalities?

Back

It indicates that the solutions are all the points above the line, satisfying the inequality (y > mx + b).

Front

What does shading below a line indicate in graphing inequalities?

Back

It indicates that the solutions are all the points below the line, satisfying the inequality (y < mx + b).

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates they are not (> or <).

Front

What is the graphical representation of the inequality y ≥ x + 4?

Back

It includes the line y = x + 4 and the region above it.

Front

Which of the following points is NOT a solution to the system: y > -x - 1 and y ≥ x + 4? (0,-1), (0,3), (4,0), (6,-2)

Back

(0,-1) is not a solution.