## Simultaneous Linear Equations

#### Aligned To Common Core Standard:

**Grade 8 Number System** - 8.EE.C.7b

What are Simultaneous Linear Equations? Linear equations, a relatively newer concept for you as you get into grade 7, is a significant tool required to use in everyday applications. These equations are very helpful in describing a relationship between two variables in the physical world. They allow scientists to make predictions and conversions and calculate rates. Graphing linear equations make the trends visible. For example: y = 2x + 1 This is a linear equation. Two linear equations having two variables (x and y) taken together to solve are called simultaneous linear equations. Example of such two equations is: 2x - 3y = 4 3x + y = 1 The solution a simultaneous equation is presented in the form of an ordered pair (x, y). The steps to solve simultaneous linear equations are as follows: Equation 1: 2x + 3y = 8, Equation 2: 3x + 2y = 7 Step # 1: Multiply each equation with a number that makes the leading co-efficient the same. Step # 2: Find the difference between the two-equations. Subtract second from the first. Step # 3: Now solve the new equation that has only one variable. Step # 4: Substitute the value of this variable in either of the equations and find the other. Step # 5: Write the answer in an ordered pair.

### Printable Worksheets And Lessons

- Solve the System Step-by-Step
Lesson- Solve the system in each case. This is a very basic
starting point for students.

- Guided Lesson - Graph
the systems to find the solution for the systems.

- Guided Lesson Explanation
- These are very straightforward questions for you to begin to tackle
with students.

- Independent Practice
- Ten problems to practice away with. Get your graph paper ready.

- Matching Worksheet - Match the systems with their graphs.

#### Homework Sheets

I start this skill in a very basic manner. A flat line is always a good place to start.

- Homework 1 - Solve this system of equations by graphing. Graph the equations, and then write the solution.
- Homework 2 - Calculate the solution by graphing.
- Homework 3 - This equation tells you that every y-value is 8. Plot some points that have a y value of 8, like (0, 8) and (1, 8), and then draw a line connecting them.

#### Practice Worksheets

"Solving systems" always makes it sound a lot more complicated than the topic really is.

- Practice 1 - See where they all meet up?
- Practice 2 - Take it all home for you.
- Practice 3 - Make the Ys equal to each other and get this one going.

#### Math Skill Quizzes

For the answers, I tried to give you a snapshot of where the graph intersection is found.