1. 6.1 Graphing Systems Unit 3 Algebra 1

2. Warm Up: Graph the following equations. y = 2x + 1 x + 2y = 12

3. Objectives: 1.Solve a system of equations by graphing. 2.Solve systems from the real world. Vocabulary: system of linear equations, solution to a system, point of intersection Solving Linear Systems by Graphing 7.1

4. We have solved equations like : We found many solutions to the equations like : Now we will find 1 solution to 2 equations together like : 3(x – 4) = 5x + 2(x – 3) = 5 – (x + 4) 2x + 4 = 12x – 4 = 5 3x + 2y = 12 y = 2x - 5

5. Vocabulary: System of Linear Equations – a group of 2 or more equations that are linear. Use a set mark { to group them. To get 1 solution, you need the same number of equations as variables. Think about our introductory activity…what did you learn? Examples:

6. HOW TO: Solving a System by Graphing Steps: 1.Graph both equations. 2.Find the intersection. 3.Check the answer. Make sure to solve for y first!

7. #1: Solve the system by graphing. Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer. (3, 4)

8. #2: Solve the system by graphing. Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer. (-3, 1)

9. #3: Solve the system by graphing. Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer. (1, 3)

10. #4: Solve the system by graphing. Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer. (-3, 6)

11. #5: SPECIAL CASES Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer. no solution

12. #6: SPECIAL CASES Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer. infinite solutions

13. You and your sister each have a savings account for college. You have $2000 and plan to deposit an additional $50 per month At the same time, your sister has a balance of $1600 and she plans to deposit $100 per month. Predict when you and your sister will have the same amount? 8 months Real Life Linear System

14. How do we solve a system by graphing? Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer. Homework 6.1 Practice Worksheet