1. Chapter 3: Linear Systems
Section 3.2: Solving Systems Algebraically

2. Section 3.2: Solving Systems Algebraically
Goal: To solve linear systems algebraically

3. Section 3.2: Solving Systems Algebraically
Issue with graphing method?
Unless the lines intersect at an exact point, the solution may have to be estimated
Solution: use another method for exact solutions!
Substitution Method
Elimination Method (aka Linear Combination)

4. Section 3.2: Solving Systems Algebraically
Substitution Method
Solve for a variable
Substitute expression into other equation and solve for the variable
Substitute value of variable into the first equation and solve for remaining variable
Check your solution!

5. Section 3.2: Solving Systems Algebraically
Examples:
What is the solution of the system of equations?
5x – 3y = -1
x + y = 3

6. Section 3.2: Solving Systems Algebraically
Examples:
What is the solution of the system of equations?
3g – 2h = -1
4g + h = 17

7. Section 3.2: Solving Systems Algebraically
Examples:
3. You are in charge of ordering labels for a small business. A company that makes custom labels charges a yearly fee plus a cost per label. You paid $375 last year for 300 labels. This year you ordered 1000 labels and paid $725. What are the yearly fee and cost per label, assuming the prices did not change?

8. Section 3.2: Solving Systems Algebraically
Homework (Part 1):
Pg. 146 #10-20 (even)

9. Section 3.2: Solving Systems Algebraically
Elimination Method (aka Linear Combination)
Align the equations vertically
Multiply one or both equations in order to have a variable be eliminated
Add the equations and solve for the remaining variable
Plug value into one of the original equations and solve for the other variable

10. Section 3.2: Solving Systems Algebraically
Examples:
What is the solution of the system of equations?
2x – 3y = 14
4x + 3y = 46

11. Section 3.2: Solving Systems Algebraically
Examples:
What is the solution of the system of equations?
7x + 5y = 2
8x – 9y = 17

12. Section 3.2: Solving Systems Algebraically
Examples:
What is the solution of the system of equations?
6x + 4y = 2
3x + 2y = -1

13. Section 3.2: Solving Systems Algebraically
Examples:
What is the solution to the system of equations?
6x – 3y = 15
-8x + 4y = -20

14. Section 3.2: Solving Systems Algebraically
Homework (Part 2)
Pg. 144 #22-42 (even)