Systems of Inequalities

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share 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 point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the x and y values of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does it mean to shade above or below a line in a graph of an inequality?

Back

Shading above a 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 difference between a solid line and a dashed line in graphing inequalities?

Back

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

Front

How do you write a system of inequalities from a word problem?

Back

Identify the constraints and objectives in the problem, then translate them into inequalities using variables to represent the quantities involved.

Front

What does the inequality y ≤ x + 4 represent graphically?

Back

It represents all points on or below the line y = x + 4 in the coordinate plane.

Front

What is the significance of the feasible region in a system of inequalities?

Back

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

Front

How can you find the vertices of the feasible region?

Back

Vertices can be found by identifying the intersection points of the boundary lines of the inequalities.

Front

What is the graphical representation of the inequality y ≥ 2x - 6?

Back

It includes the line y = 2x - 6 and all points above this line.

Front

How do you solve a system of inequalities graphically?

Back

Graph each inequality on the same coordinate plane, shade the appropriate regions, and identify the overlapping area as the solution.