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

How do you determine if a line is solid or dashed in graphing inequalities?

Back

A solid line is used for inequalities that include equal to (≥ or ≤), while a dashed line is used for inequalities that do not include equal to (> or <).

Front

What does it mean to shade above or below a line in graphing inequalities?

Back

Shading above the line indicates that the solutions are greater than the line (y > mx + b), while shading below indicates that the solutions are less than the line (y < mx + b).

Front

What is the solution to the inequality y < 2x + 3?

Back

The solution is the region below the line y = 2x + 3, not including the line itself.

Front

How do you graph the inequality y ≥ -x + 1?

Back

Graph the line y = -x + 1 with a solid line and shade above the line.

Front

What is the significance of the point (1, 0) in the context of a system of inequalities?

Back

The point (1, 0) is a solution to the system if it satisfies all inequalities in the system.

Front

What does the term 'feasible region' refer to in systems of inequalities?

Back

The feasible region is the area on the graph where all the inequalities overlap, representing all possible solutions.

Front

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

Back

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

Front

What is the first step in solving a system of inequalities by graphing?

Back

The first step is to graph each inequality on the same coordinate plane.

Front

What does the inequality y < 3 represent on a graph?

Back

It represents all points below the horizontal line y = 3, not including the line itself.