1. Ch 5.3 Elimination (addition)
Objective:
To solve a system of linear equations using elimination with addition.

2. Review Graphic Method Substitution Method - Time consuming
If b = a
and b = c
solution
then a = c.
- Time consuming
- Not always convenient
- Not always accurate

3. Definition Rules Check Your Answers! Eliminate: Get rid of
Rearrange the equations so that “like” terms are lined up.
Add (or subtract) the two equations to each other to eliminate a variable.
3) Solve for the remaining variable.
4) Plug in your solution into either of the equations to solve for the other variable.
Check Your Answers!
Plug in the x and y solutions into BOTH equations to verify that they both make TRUE statements.

4. Solve using elimination
Example 1
Solve using elimination
p + 4q = 23
-p + q = 2 +
-p + q = 2
-p +( ) = 2 5
5q = 25
-p = -3
q = 5
(-1)
(-1)
p = 3
p = 3, q = 5

5. Solve using elimination
Example 2
Solve using elimination
x + 3y = 3
x + 6y = 3 -
x + 3y = 3
( )
x + 3( ) = 3
-3y = 0
y = 0
x = 3
x = 3, y = 0

6. Solve using elimination
Example 3
Solve using elimination
t + r = 1
2r - t = 2
t + r = 1
-t + 2r = 2 +
3r = 3
t + r = 1
t + ( ) = 1 1
r = 1
t = 0
r = 1, t = 0

7. Solve using elimination
Example 4
Solve using elimination
2x + y = 6
3x - y = 4 +
2x + y = 6
5x = 10
2( ) + y = 6 2 4
x = 2
y = 2
x = 2, y = 2

8. Solve using elimination
Example 5
Solve using elimination
x + 3y = 5
-x + y = 3 +
x + 3y = 5
4y = 8
x + 3( ) = 5 2 6
y = 2
x = -1
x = -1, y = 2

9. Classwork 7x + 4y = -16 9x – 7y = -4 -7x – 6y = -4 -9x + y = 161)
7x + 4y = -16 2)
9x – 7y = -4
-7x – 6y = -4
-9x + y = 16 3)
7x – 8y = 14 4)
-3x + 6y = -6
7x – 9y = 7
-8x + 6y = 4

10. 6x + 3y = -15 2x – 6y = 24 2x + 3y = -11 -3x - 6y = 24 -x + 2y = 65)
6x + 3y = -15 6)
2x – 6y = 24
2x + 3y = -11
-3x - 6y = 24 7)
-x + 2y = 6 8)
-4x + 3y = 21
x + 8y = -26
-4x + 4y = 24