1. Elimination Method Day 1
Today’s Objective:
I can solve a system using elimination.

2. x + y = 7 x – y = 3 (5, 2) x – y = 3 + y + y x = 3 + y x + y = 7
1. Solve for 1 variable
x + y = 7
x – y = 3
2. Substitute the variable you just solved for into the other equation AND solve.
Substitution review
3. Solve for the other variable (substitute)
4. Write the ordered pair
Step 2
Step 1
Step 3
x + y = 7
( ) + y = 7
3 + y + y = 7
3 + 2y = 7
2y = 4
y = 2
x= 3 + y
x = 3 + ( )
x = 3 + 2
x = 5
x – y = 3
+ y y
x = 3 + y
3 + y 2
Step 4
(5, 2)

3. x + y = 7 x – y = 3 2x = 10 x = 5 (5, 2) x+ y = 7 ( ) + y = 7 -5 -5
Solve each system using ELIMINATION
Identify one variable in each equation that has the same number but with opposite signs.
Step 2
2x = 10
2. Add the 2 equations
3. Solve for one variable
x = 5
Solve for the other variable. (substitute into one of the original equations).
Step 3
x+ y = 7
( ) + y = 7
y = 2
Step 4
5. Write the ordered pair. 5
(5, 2)
Step 5

4. 2x – y = -5 -2x – 5y = 11 -6y = 6 (-3, -1) y = -1 -2x – 5y = 11
Identify one variable in each equation that has the same number but with opposite signs.
2. Add the 2 equations
3. Solve for one variable
Step 2
-6y = 6
Solve for the other variable. (substitute into one of the original equations).
y = -1
Step 3
5. Write the ordered pair.
-2x – 5y = 11
-2x – 5( ) = 11
-2x + 5 = 11
-2x = 6
x = -3
Step 4 -1
(-3, -1)
Step 5

5. 10x – 35y = 15
-10x + 8 y = 12
Identify one variable in each equation that has the same number but with opposite signs.
2. Add the 2 equations
3. Solve for one variable
Step 2
-27y = 27
Solve for the other variable. (substitute into one of the original equations).
y = -1
Step 3
5. Write the ordered pair.
-10x + 8y = 12
-10x + 8( ) = 12
-10x – 8 = 12
-10 x = 20
x = -2
Step 4 -1
(-2, -1)
Step 5

6. I can solve a system using elimination.
Assignment
Book pg 382: 7, 8,11, 54, 55
Select answers
7. (4,5)
(22,7)
11. ( 3,15)

7. 2x – 3y = 5 x – 2y = 4 -2( ) 2x – 3y = 5 -2x + 4y = -8 y = -3
Step 4 (substitute)
x – 2y = 4
x – 2( ) = 4
x + 6 = 4
x = -2
-2( ) -3
Rewrite both equations
2x – 3y = 5
-2x + 4y = -8
y = -3
Step 2
(add the equations)
Step 5
(ordered pair)
( -2, -3)
Step 3
Solve for 1 variable
y = -3

8. 4( ) 2x + 3y = 10 3x – 4y = -2 3( ) 8x + 12y = 40 9x – 12y = -6
4( )
2x + 3y = 10
3x – 4y = -2
Step 4
2x + 3y = 10
2( ) + 3y = 10
4 + 3y = 10
3y = 6
y = 2
3( ) 2
8x + 12y = 40
9x – 12y = -6
17x = 34
Step 2
Step 5
(2, 2)
Step 3
x = 2

9. 2( ) 3x + 2y = 17 2x + 5y = 26 -3( ) 6x + 4y = 34 -6x – 15y = -78
2( )
3x + 2y = 17
2x + 5y = 26
Step 4
3x + 2y = 17
3x + 2( ) = 17
3x + 8 = 17
3x = 9
x = 3
-3( ) 4
6x + 4y = 34
-6x – 15y = -78
-11y = -44
Step 2
Step 5
(3, 4)
Step 3
y = 4

10. Assignment day 2
Book pg 382: 9,10,12,15-20,22-24
(note: , look at previous notes for 1 solution, infinitely many solutions, or no solutions)
9. (1,5) (3,1) (2,-1)
10.(6,3) (1,2) (4,7)
17. (5,3)
12. (4,3) (3,4)