1. 5.3 Elimination Using Addition and Subtraction
Objective: Each student will understand when to solve
a system by elimination using addition and subtraction.
Academic Standard:2.4d Solve systems of equations.
Algebra 1

2. Notes: Another algebraic method used to solve systems of equations.
- two equations are combined by either
addition or subtraction to eliminate
one of the variable
- then substitute that value back into
either of the original equations.
- the solution is written as an ordered pair
If the coefficients of one of the
variables are additive inverses , or
opposites.
variables are the same.
What is the Elimination Method?
When should you use addition?
When should you use subtraction?

3. Example 1 : Use elimination to solve the system
5x + 3y = 6
-5x + y = 2
+ -5x + y = 2
4y = 8
y = 2
5x + 3(2) = 6
5x + 6 = 6
5x = 0
x = 0
Since 5x and -5x are additive inverses
we will add the two equations together.
Add equations
Divide both sides by 4
y = 2
Substitute 2 in for y in one of the original equations
Subtract 6 from both sides
Divide by 5 on both sides
Solution (0 , 2)

4. Practice 1: Use elimination to solve the system of equations.
3x – 5y = -16
2x + 5y = 31
-4x – 3y = -3
4x – 5y = 5

5. Example 2: Twice a number added to another number is 18
Example 2: Twice a number added to another number is 18. Four times the first number minus the other number is 12. Find the numbers?
Define variables: x = first number y = second number
Write a verbal expression for each equation
Twice a number added to another number is
Four times the first number minus the other number is
Write an algebraic expression for each equation x + y = 18
4x + y = 12
Solve using elimination

6. Assignment
Pg 268 (1-4, 8-16 even, 37-42)