1. 3.2 – Solving Systems Algebraically

2. The goal of substitution is to put on equation into the other so there is only one variable to solve for.
Substitution

3. Steps for Substitution
Solve 1 of the equations for 1 of its variables
Substitute the expression from Step 1 into the other equation and solve.
Substitute the value from Step 2 into an equation and solve for the remaining variable.
Steps for Substitution

4. Example: Solve the linear system. 3x – y = 13 2x + 2y = -10

5. -x + 3y = 1 4x + 6y = 10

6. The goal with linear combination is to get one variable to cancel.
Then you will only have 1 equation with 1 unknown and you can solve for it.
Linear Combination

7. What would you have to add to the following terms for their sum to be zero?3x
-2y -x
10y
Think Opposite!

8. Think Opposite! 3x, x -4y, 2y 5x, 3x
2 terms are given below. Find what you could multiply one (or two) term(s) by so that the sum of the two terms is zero.
3x, x
-4y, 2y
5x, 3x
Think Opposite!

9. Steps to Solve by Linear Combination
Make sure all like terms are lined up.
Multiply one or both equations by a constant so 1 variable will cancel when the 2 equations are added.
Add the two equations together and solve.
Substitute answer into an original equation to find the other variable.

10. Solve the following linear systems.
1. 2x – 6y = 19 -3x + 2y = 10

11. 2. 3x + 2y = 10 5x - 7y = -4

12. 3. 6x – 4y = 14 -3x + 2y = 7

13. 4. 9x – 3y = 15 -3x + y = -5

14. Suppose you are going on vacation and leaving your dog in a kennel
Suppose you are going on vacation and leaving your dog in a kennel. The Bowowery charges $25 per day, which includes a one-time grooming treatment. The Poochpad charges $20 per day and a one-time fee of $30 for grooming.
Write a system of equations to represent the cost, c, for d days that your dog will stay at the kennel.
Find the number of days for which the costs are the same.
If your vacation is a week long, which kennel should you choose? Explain

15. You and your business partner are mailing advertising flyers to your customers. You address 6 flyers each minute and have already done 80. Your partner addresses 4 flyers each minute and has already done 100. Write a system of equations and find when you will have addressed the same number of flyers.