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 graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the appropriate region for each inequality, and the solution is where the shaded regions overlap.

Front

What does the solution to a system of inequalities represent?

Back

The solution to a system of inequalities represents all the points (x, y) that satisfy all inequalities in the system.

Front

What is the difference between a solution and a feasible solution in a system of inequalities?

Back

A solution is any point that satisfies the inequalities, while a feasible solution is a solution that also meets any additional constraints, such as non-negativity.

Front

What does the inequality y > mx + b represent?

Back

This inequality represents the region above the line y = mx + b, where m is the slope and b is the y-intercept.

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 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. Points on the line are included if the inequality is ≤ or ≥.

Front

What does the inequality x + y ≤ 6 represent in a real-world context?

Back

This inequality could represent a constraint on resources, such as time or materials, where the total used cannot exceed 6 units.

Front

How can you express a real-world problem as a system of inequalities?

Back

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

Front

What is the graphical representation of y < 2?

Back

The graphical representation of y < 2 is a horizontal line at y = 2 with a dashed line, shading the area below the line.