1. Solving Linear Equations
Elimination
S. Calahan

2. x + 2y = 5 -x + y = 13 Example Eliminate the x since the
co-efficients are opposites.

3. x + 2y = 5
-x + y = 13
3y = 18

4. 3y = 18
y = 6

5. Use one of the original equations to substitute y =6. x + 2y = 5
y = 6, so find x
Use one of the original equations to substitute y =6.
x + 2y = 5
x + 2(6) = 5
x + 12 = 5

6. x + 12 = 5
x + 12 = 5
Solve = -12
x = - 7
Since y = 6 and x = -7, then the solution is
(-7, 6)

7. Solve the system of equations.
2x – 6y = 6
2x + 3y = 24
Notice the x
co-efficients are the same.

8. Subtract the equations 2x – 6y = 6 - (2x + 3y = 24)
Distribute the negative

9. Now add
2x – 6y = 6
-2x - 3y = -24
-9y = - 18
y = 2

10. Using one of the 2 equations solve for x
2x – 6y = 6
Remember y = 2
So, 2x – 6(2) = 6
2x – 12 = 6
2x = 18

11. 2x – 12 = 6
2x = 18
x = 9

12. So the solution is
(9, 2)