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6.1 Graphing Systems

Learn to solve systems of linear equations by graphing, with examples and step-by-step instructions. Apply these skills to real-world scenarios. Practice graphing equations and finding intersections for solutions.

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6.1 Graphing Systems

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  1. 6.1 Graphing Systems Unit 3 Algebra 1

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

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

  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: 2x + 4 = 12 x – 4 = 5 3(x – 4) = 5 x + 2(x – 3) = 5 – (x + 4) y = 2x - 5 3x + 2y = 12

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

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

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

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

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

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

  11. #5: SPECIAL CASES • Solve a System by Graphing • Graph both equations. • Find the intersection. • Check the answer. nosolution

  12. #6: SPECIAL CASES • Solve a System by Graphing • Graph both equations. • Find the intersection. • Check the answer. infinitesolutions

  13. Real Life Linear System 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

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

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