1. Systems of Linear Equations Solving by Elimination (Addition)

2. Homework Answers - Substitution
(2,1)
(4,3)
(1,2)
(-4,3)
(3,-2)
(2,3)
(-3,-6)
(3,-4)
(0,-2)
(0,-3)
11. (7,-2)
12. (-4,-1)
13. No Solution
14. (-3,-2)
15. (-3,2)
16. (7,6)
17. (-2,1)
18. (3,2)
19. (-5,1)
20. (4,1)

3. Racing Review
Is (3,4) a solution to the following system of equations?
4x-2y=4
y=4x-8
4(3)-2(4)=4
12-8=4
4=4 OK
4=4(3)-8
4=12-8
YES!

4. Racing Review
What is the solution to this system of equations (use substitution)?
x-6y=3
3y=x-3
By substitution…
Isolate variable:
x=3+3y
Plug into other eqn:
3+3y-6y=3
3-3y=3
-3y=0
y=0
Plug ans. into eqn
x-6(0)=3
x=3
(3,0)

5. Random Fact!
If you have 3 quarters, 4 dimes, and 4 pennies, you have $1.19. You also have the largest amount of money in coins without being able to make change for a dollar.

6. NOTES The method is very similar to solving a simple equation.
The last way to solve a system of equations that we will consider is by the ELIMINATION or ADDITION method.
The method is very similar to solving a simple equation.

7. Notes - Example 1 Solve the following system of equations:
y=12+6x & -y+x=3
1) Line the equations up like an addition problem, making sure the x’s, y’s, and numbers are all together. Then, add the the equations just like you add numbers - remember, you can only combine like terms! The goal is to get rid of one of the variables.
y=12+6x  y-6x=12
y - 6x = 12
 -y + x = 3
0 - 5x = 15

8. Notes - Example 1, cont. From previous step: 0 - 5x = 15
2) Solve for the variable that is now alone.
-5x=15 (divide both sides by -5)
x=-3
3) Plug this value into one of the original equations to find the missing value
y=12+6x  y=12+6(-3)  y=-6
ANSWER: (-3,-6)

9. Random Fact!
Dentists have recommended that a toothbrush be kept at least 6 feet (2 m) away from a toilet to avoid airborne particles resulting from the flush.

10. Notes - Example 2 Solve the following system of equations:
2x-3y=6 & x+y=-12
Line the equations up, and get ready to add!
2x - 3y = 6
 x + y = -12
Now what do you do? How do you add the equations when the numbers don’t easily cancel out?
You need to multiply one of the equations by a number so that one of the variables will cancel out when you add. What number do you think we should multiply by, and which equation???

11. Notes - Example 2, cont.
Right! You can multiply the second equation by -2 to get rid of the x’s or 3 to get rid of the y’s. Let’s multiply by -2. Remember, what you do on one side, you must do on the other.
2x - 3y = 6
 -2*(x + y) = (-12)*-2
 -2x - 2y = 24
0 - 5y = 30
Solve for x (divide both sides by -5)  y=-6
Plug x into one of the equations  x+y=-12
 x+(-6)=-12  x= ANSWER: (-6,-6)

12. Random Fact!
When snakes are born with two heads, they fight each other for food.

13. Classwork! :)
Find the solution to the following systems of equations by elimination.
A B C
y=x+1
2y=3x
y=5x-1
2y=3x+12
y=3x+1
4y=12x+4
Check your answers!

14. Classwork! :)
Find the solution to the following systems of equations by elimination.
A B
(2,3) (2,9) C
Infinite number of solutions - they are the same line!
Check your answers!

15. Homework Answers - Elimination
(6,-6)
(7,-1)
(10,-1)
(-1,-1)
(-1,3)
(-1,-8)
(5,6)
(6,-9)
(1,4)
(9,5)
(-4,-4)
(2,-5)
13. (0,-1)
14. (4,-2)
15. (8,-1)
16. (0,-2)
17. (1,-2)
18. (-6,0)
19. (-1,-5)
(-2,-4)
(-6,4)
Infinite # of Solutions b/c lines are the same
(2,0)
(-1,1)