1. 6.3 – Solving Systems of Linear Equations by Elimination.
Definitions of the Day (DODs)
Review of Ch 6 Systems of Equations So Far…
6.1 Graphing
6.2 Substitution Method
6.3 Elimination Method

2. Definition: Elimination Method –Eliminate one of the variables by adding (or subtracting) the equations of the system.  
Let us Explore… x y 10 + =
Top Equation + x ( - y = ) + 36
Bottom Equation
2x = 46
Y has been ELIMINATED x 23
, y =-13 =
Solve for x,
Substitute for y

3. Steps to the Elimination Method!!
Pick One Variable to Eliminate! (Either x or y.)
2. Eliminate the Variable by adding or subtracting the equations together.
3. Substitute & Solve for the last Variable.

4. Example #1
5x - 6y = -32
3x + 6y = 48

5. Example #2
X+Y=6
X+3Y=10

6. WARNING!
WE MAY NEED TO MANIPULATE ONE OF THE EQUATIONS BEFORE SOLVING FOR A VARIABLE!

7. Example #3 (One Solution)
3x + 4y = -10
5x - 2y = 18

8. Example #4 (No Solution)
2x - 3y = 6
6x - 9y = 9

9. Example #5 (Infinitely Many Solutions)
x + 4y = 1
3x + 12y = 3

10. Your Turn!! Solve by ELIMINATION 1. X+ y = 12 2. 4x - 2y = 6

11. Sentence Frames
The Goal of Solving a System of Equations by Elimination is __________________________________________________________________________________________________
The Three methods for solving a System of Equations are
1. _______________
2. _______________
3. _______________