1. Problem of the Day y= - 1 2 x – 7 2x – 6y = 12
Solve the following system algebraically, using substitution:
y= x – 7
2x – 6y = 12

2. Solving Algebraically
by Elimination
I sure do love that trusty substitution!
Look for a pair
of matching
opposites
x + 3y = 8
6x – 3y = 27 +
7x = 35 7
But sometimes there’s an easier way! 7
x + 3y = 8
x = 5
5 + 3y = 8
(5, 1)
3y = 3
y = 1

3. Try shoveling a sidewalk with that thing buddy!
Problem of the Day
y= x – 7
2x – 6y = 12
What the deuce!?
Mwahahahaha!
Try shoveling a sidewalk with that thing buddy!

4. 4( ) 2x + y = 3 7x – 4y = 18 8x + 4y = 12 7x – 4y = 18 Find an LCM
Anyway, where were we?
If you don’t have matching opposites, you can make them match.
4( )
2x + y = 3
7x – 4y = 18
8x + 4y = 12
7x – 4y = 18
Find an LCM
to distribute

5. Steps to Solving by Elimination
Look for equal opposites or a pair
that’s easy to manipulate
Step 1
Distribute the coefficient you need
across one or both equations to make
equal opposites
Step 2
Step 3
Add equations together and cancel pair
Step 4
Solve for one variable
Plug answer back in to find other
variable
Step 5

6. Practice
3x + 4y = 1
2x + 4y = 6
3x + 2y = -1
4x – 5y = -32

7. Solving Equations Algebraically
Using Elimination
Look for ___________________________________________________
x + 3y = 8
6x – 3y = 27
If you don’t have matching opposites, you can make them match: _________________________
________________________________________________________________________
2x + y = 3
7x – 4y = 18
Steps to solving systems by ELIMINATION:
Step 1: _______________________________________________________________________
_______________________________________________________________________
Step 2: _______________________________________________________________________
Step 3: _______________________________________________________________________
Step 4: _______________________________________________________________________
Step 5 : _______________________________________________________________________
3x + 4y = x + 2y = -1
2x + 4y = x – 5y = -32