1. System of Equations Elimination Method
Presented Mr. Laws
8th Math JCMS

2. Standard/Goal
8.EE.8a – Solve systems of equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

3. Essential Questions
Using math principles, how do I solve a system of equations using the elimination method?

4. What is the Elimination Method?
The elimination method is used to solve system of equations by eliminating either the x or y variable of one equation.
The both equations in the system is written in standard form.

5. Solving System by Elimination
Example # 1
Step 1: Look for a variable you can eliminate in the system.
x + 4y = 8
3x – 4y = 8
Step 2: Since there is positive 4y in the 1st equation and a negative 4y in the second equation, the y variable can be eliminated.
4x = 16 4
Step 3: Add the x variable: 1x + 3x = 4x; constant: = 16
( 4, 1)
x = 4
Step 4: Solve for x
4 + 4y = 8
Step 5: Replace the value of x in one of the equations to find the value of y. -4
4y = 4 4
y = 1
Step 6: Solve for y

6. Solving System by Elimination
Example # 2
Step 1: Can’t eliminate x or y, so pick an easy variable to eliminate:
2x + 5y = 9
x – 3y = 10
Step 2: Eliminate x in the second equation by multiplying the equation by -2:
-2(x – 3y = 10)
Step 3 : Eliminate the x variable and solve for y.
-2x + 6y = - 20
2x + 5y = 9
11y = -11 11
y = -1
2x + 5 (-1) = 9
2x – 5 = 9
2x = 14
x = 7
Step 4: Replace the value of y in one of the equations and solve for x.
( 7, -1)

7. Solving System by Elimination
Step 1: Find the least common multiple (LCM) of one the variables.
Example # 3
5x + 3y = 2
4x + 2y = 10
Step 2: LCM of 3 (y) and 2 (y) = 6 Multiply the 1st equation by -2 and the 2nd equation by 3 to eliminate the y variable.
-2(5x +3y = 2)
3(4x +2y = 10)
Step 3 : Use the distributive property to change both equations.
-10x – 6y = -4
12x + 6y = 30
5(13) + 3y = 2
Step 4 : Eliminate the y variable and solve for x.
65 + 3y = 2
Step 5: Replace the value of x in one of the equations and solve for y.
2x = 26
3y = -63
y = -21
x = 13
( 13, -21)

8. Summary What have you learn in this lesson?
What are some important things to remember about system of equations?
Do you have additional questions concerning this lesson?