Download Linear Combination Method for solving Linear Systems

Elimination Method for solving Linear Systems
Step 1:
Step 2:
Step 3:
Step 4:
Name:
Find or Make Opposites (coefficients for x or y)
Add the equations and solve for the remaining letter.
Plug your answer into either of the original equations.
Write your answer as an ordered pair and check.
Example:
3x + 5y = 13 I don’t see opposites, so I decide to make 3x and 2x opposites…
2x + 7y = 16 I multiply the entire top row by 2 and the bottom by -3…
one of them has to be negative, but it doesn’t matter which one
6x + 10y = 26
Don’t forget to multiply the 13 and 16 as well.
-6x – 21y = -48
Now I have 6x and -6x, so I can add to cancel.
0 – 11y = -22
Drop the zero
-11y = -22
Divide by -11
y=2
3x + 5(2) = 13
3x + 10 = 13
3x = 3
x=1
Answer (1, 2)
1. 3x – 2y = 8
-3x + 3y = -3
2. 2x – 4y = 4
-3x + 4y = -8
3. 2x + 5y = -1
-2x – 3y = 3
4. 2x + 5y = -14
-3x – 5y = 11
Plug your answer into either equation, I chose the top one.
subtract 10 from both sides.
divide by 3 on both sides
write your answer as an ordered pair.
5. 2x – 3y = 8
-4x + 5y = -10
6. 3x – 6y = 3
-4x + 3y = -9
7. 9x – 2y = 21
-3x + 5y = 6
8. 6x + 6y = -12
-5x – 2y = 22
9. 4x + 5y = 2
-6x - 2y = -14
10. 7x + 6y = -12
-4x – 9y = -21