6.3 – solving systems of linear equations by elimination. definitions of the day (dods) review of...
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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
Review of Ch 6 Systems of Equations So Far…
6.1 Graphing
6.2 Substitution Method
6.3 Elimination Method
Definition: Elimination Method –Eliminate one of the variables by adding (or subtracting) the equations of the system.
Definition: Elimination Method –Eliminate one of the variables by adding (or subtracting) the equations of the system.
Let us Explore…Let us Explore…
+ =x y 10x - y = 36
Top Equation
Bottom Equation( )+ 2x = 46
+
Y has been ELIMINATED
x =23, y =-13 Solve for x, Substitute for y
Steps to the Elimination Method!!Steps to the Elimination Method!!
1. 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.
Example #1Example #1
5x - 6y = -323x + 6y = 48
X+Y=6
Example #2Example #2
X+3Y=10
WARNING!WARNING!
• WE MAY NEED TO MANIPULATE ONE OF
THE EQUATIONS BEFORE SOLVING FOR
A VARIABLE!
3x + 4y = -105x - 2y = 18
Example #3(One Solution)Example #3(One Solution)
6x - 9y = 9
Example #4(No Solution)Example #4(No Solution)
2x - 3y = 6
x + 4y = 1
Example #5(Infinitely Many Solutions)
Example #5(Infinitely Many Solutions)
3x + 12y = 3
Solve by ELIMINATION
1. X+ y = 12 2. 4x - 2y = 6
x - y = 2 -2x + y = -3
Solve by ELIMINATION
1. X+ y = 12 2. 4x - 2y = 6
x - y = 2 -2x + y = -3
Your Turn!!Your Turn!!
Sentence FramesSentence Frames
1. The Goal of Solving a System of Equations by Elimination is __________________________________________________________________________________________________
2. The Three methods for solving a System of Equations are
1. _______________
2. _______________
3. _______________
1. The Goal of Solving a System of Equations by Elimination is __________________________________________________________________________________________________
2. The Three methods for solving a System of Equations are
1. _______________
2. _______________
3. _______________