1. Solving by Substitution Method or Elimination (Addition) Method
Section 8.2
Solving by
Substitution Method or Elimination (Addition) Method

2. Substitution Method
An algebraic method to solving the system of equations.
This is the most popular method, you have worked with it before, but did not know.
Places one equation into the other equation, to make one large equation that contains only one unknown variable.
Best method when one variable is already isolated.

3. Substitution Method Steps Isolate one variable of one equation.
Substitute that answer into the same variable of the other equation.
Solve for the unknown
If variable remains
plug answer into one of the two original equations and find the other unknown.
Then write answer in ordered form
If the variables cancel out, you have either
no solution : False Statement
infinite solutions : True Statement

4. Solve the system of linear equations.
Substitution Method
Solve the system of linear equations.

5. Solve the system of linear equations.
Substitution Method
Solve the system of linear equations.

6. Solve the system of linear equations.
Substitution Method
Solve the system of linear equations.

7. Solve the system of linear equations.
Substitution Method
Solve the system of linear equations.

8. Addition / Elimination Method
Is the go to method when you do not want to work with fractions or decimals.
Must be in standard form Ax + By = C
Has two titles because both titles explain what you do
Addition : You will combine two equations.
Elimination : You will cancel a variable out.

9. Addition / Elimination Method
Steps
Write each equation in standard form.
Find the variable you want to eliminate
Make the two variables opposite by multiplying each equation by least common multiple.
Add the two equations together
If the variable cancels
And you have a false statement you have no solution.
And you have a true statement you have infinite solutions.
If the variable remains
solve for the unknown
Then plug value into one of the original equations and find the other unknown.

10. Addition / Elimination Method
Solve the system of linear equations.

11. Addition / Elimination Method
Solve the system of linear equations.

12. Addition / Elimination Method
Solve the system of linear equations.

13. Addition / Elimination Method
Solve the system of linear equations.

14. Homework
Section 8.2
23, 40, 47, 48, 53, 54