Create a lesson plan of a system of linear equations with two variables. Include pre-requisite material. Include several practice examples and a few examples worked out. Set up for Arizona State standards 8th grade. Include a short worksheet at the very end with a separate solutions worksheet.
**Lesson Plan: Systems of Linear Equations with Two Variables**

**Grade Level:** 8th Grade

**Arizona State Standards:**

* 8.EE.8: Analyze and solve systems of linear equations.
* 8.EE.7: Solve linear equations in one variable.

**Pre-requisite Material:**

* Students should have a solid understanding of:
	+ Linear equations in one variable (8.EE.7)
	+ Graphing linear equations on a coordinate plane
	+ Slope-intercept form (y = mx + b)

**Objective:**

* Students will be able to analyze and solve systems of linear equations with two variables using substitution, elimination, and graphing methods.
* Students will understand the concept of a solution to a system of linear equations and how to represent it graphically.

**Materials:**

* Whiteboard and markers
* Graph paper
* Rulers
* Pencils
* Worksheet with practice problems
* Solutions worksheet

**Procedure:**

**Introduction (10 minutes)**

1. Review linear equations in one variable and graphing on a coordinate plane.
2. Introduce the concept of a system of linear equations with two variables.
3. Write a simple system of linear equations on the board, such as:
	* 2x + 3y = 7
	* x - 2y = -3
4. Ask students to share what they notice about the system.

**Direct Instruction
Objective: Students will be able to solve a system of two linear equations with two variables. 

Materials:
- Pencils, Pens, and Erasers
- Graph paper
- Calculators (optional)

Pre-requisite material:
- Solving linear equations 
- Understanding the concept of a variable

Lesson: 
1. Introduce the concept of a system of equations and variables.
2. Review solving linear equations.
3. Show examples of solving a system of two equations with two variables.
4. Give students practice examples with step-by-step instructions.
5. Provide a worksheet with a separate solutions worksheet.
6. Review answers and discuss solutions.