# Systems of Linear Inequalities Worksheets

What are Systems of Linear Inequalities? Once you have gotten to know how to deal with linear Inequalities, it's time to take the next step and move forward with to learn other advanced concepts. You can now move on to solving the systems of linear inequalities. A system of linear inequalities in two variables refers to or consists of at least two inequalities in the same variable. The solution to a system of linear inequalities is the same as the ordered pair used in linear inequalities. It is the solution to all inequalities in the system. And the graph of linear inequality is the graph for all solutions/ordered pairs in the system. For example, 2x - 3y ≤ 12. When dealing with the system of linear inequalities, you deal with all the inequalities at once. The common practice or standard is that you start with two or three inequalities at a time. The technique for solving these inequalities is relatively simple. However, the best way to solve them is to solve ass many inequalities as possible in one go.

• ### Basic Lesson

Demonstrates how to solve complex inequalities graphically. If the point makes the inequality true, shade that side of the line. If the point does not make the inequality true, shade the opposite side of the line.

• ### Intermediate Lesson

Explores how to solve complex inequalities graphically and with the use of dashed lines. Draw line dashed if the inequality is < or >.

• ### Independent Practice 1

Solve the following system of inequalities graphically. The answers can be found below.

• ### Independent Practice 2

Features another 20 Systems of Linear Inequalities problems.

• ### Homework Worksheet

Systems of Linear Inequalities problems for students to work on at home. Example problems are provided and explained.

• ### Topic Quiz

10 Systems of Linear Inequalities problems. A math scoring matrix is included.

• ### Homework and Quiz Answer Key

Answers for the homework and quiz.

• ### Lesson and Practice Answer Key

Answers for both lessons and both practice sheets.

#### Dull Numbers?

"Nonsense," replied Ramanujan. "The number isn't dull at all. It's quite interesting. It's the smallest number that can be expressed as the sum of two cubes in two different ways." (Ramanujan recognized that 1729 = 13 + 123 as well as 93 + 103.)