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 graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then shade the region that satisfies the inequality.

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it satisfies all inequalities in the system, meaning it lies in the shaded region of the graph.

Front

How can you determine 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 significance of the feasible region in a system of inequalities?

Back

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

Front

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

Back

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

Front

How do you find the area of a rectangle given its perimeter and a relationship between length and width?

Back

Use the perimeter formula (P = 2L + 2W) and the relationship (L = 3W) to set up equations. Solve for W, then find L, and finally calculate the area (A = L * W).

Front

What is the perimeter of a rectangle?

Back

The perimeter of a rectangle is the total distance around the rectangle, calculated as P = 2L + 2W, where L is the length and W is the width.

Front

How do you solve a word problem involving a system of equations?

Back

Identify the variables, set up equations based on the problem's information, and solve the system using substitution or elimination.

Front

What is the relationship between the number of legs and animals in a word problem?

Back

In problems involving animals, each type of animal has a specific number of legs (e.g., horses have 4 legs, chickens have 2). Use this information to set up equations.