Transcript 6.3 – Solving Systems of Linear Equations by Elimination.

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
Definition: Elimination Method –
Eliminate one of the variables by
adding (or subtracting) the
equations of the system.
Let us Explore…
x + y = 10
+ (x - y = 36)
2x = 46
x = 23 , y =-13
Top Equation
+
Bottom Equation
Y has been
ELIMINATED
Solve for x,
Substitute for y
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 #1
5x - 6y = -32
3x + 6y = 48
Example #2
X+Y=6
X+3Y=10
WARNING!
• WE MAY NEED TO
MANIPULATE ONE OF
THE EQUATIONS
BEFORE SOLVING FOR
A VARIABLE!
Example #3
(One Solution)
3x + 4y = -10
5x - 2y = 18
Example #4
(No Solution)
2x - 3y = 6
6x - 9y = 9
Example #5
(Infinitely Many Solutions)
x + 4y = 1
3x + 12y = 3
Your Turn!!
1.
Solve by ELIMINATION
X+ y = 12
2. 4x - 2y = 6
x-y=2
-2x + y = -3
Sentence Frames
1.
2.
The Goal of Solving a System of Equations by Elimination is
_________________________________________________
_________________________________________________
The Three methods for solving a System of
Equations are
1. _______________
2. _______________
3. _______________