Elimination Method for Solving a System of Linear Equations

Examples, worksheets, videos and solutions to help Grade 8 students learn the elimination method for solving a system of linear equations.

New York State Common Core Math Grade 8, Module 4, Lesson 28

Worksheets for Grade 8

Lesson 28 Student Outcomes

• Students learn the elimination method for solving a system of linear equations.
  
• Students use properties of rational numbers to find a solution to a system, if it exists, through computation using substitution and elimination methods.

Lesson 28 Student Summary
Systems of linear equations can be solved by eliminating one of the variables from the system. One way to eliminate a variable is by setting both equations equal to the same variable, then writing the expressions equal to one another.

Another way to eliminate a variable is by multiplying each term of an equation by the same constant to make an equivalent equation. Then use the equivalent equation to eliminate one of the variables and solve the system. Once a solution has been found, verify the solution graphically or by substitution.

The following diagram shows an example of solving by elimination. Scroll down the page for more examples and solutions on how to solve by elimination.

 

Lesson 28 Classwork
Example 1
Use what you noticed about adding equivalent expressions to solve the following system by elimination:
6x - 5y = 21
2x + 5y = -5

Example 2
Solve the following system by elimination:
-2x + 7y = 5
4x - 2y = 14

Example 3
Solve the following system by elimination:
7x - 5y = -2
3x - 3y = 7

Exercises
Each of the following systems has a solution. Determine the solution to the system by eliminating one of the variables.
Verify the solution using the graph of the system.

1. 6x - 7y = -10
   3x + 7y = -8
2. x - 4y = 7
   5x + 9y = 6
3. 2x - 3y = -5
   3x + 5y = 1

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