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Lesson 7-1

Lesson 7-1. Graphing Systems of Equations. Transparency 1. Click the mouse button or press the Space Bar to display the answers. Transparency 1a. Objectives. Determine whether a system of linear equations has 0, 1, or infinitely many solutions Solve a system of equations by graphing.

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Lesson 7-1

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  1. Lesson 7-1 Graphing Systems of Equations

  2. Transparency 1 Click the mouse button or press the Space Bar to display the answers.

  3. Transparency 1a

  4. Objectives • Determine whether a system of linear equations has 0, 1, or infinitely many solutions • Solve a system of equations by graphing

  5. Vocabulary • System of equations – two or more equations • Consistent – a system of equations that has at least one ordered pair that satisfies both equations • Inconsistent – a system of equations with no ordered pair that satisfies both equations • Independent – a system of equations with exactly one solution • Dependent – a system of equations that has an infinite number of solutions

  6. y y y System of Equalities • Solutions of two linear equations result in: No Solutions One Solution Infinite Solutions x x x Because (graphically): Lines are parallel Lines Intersect Same Line

  7. Use the graph to determine whether the system has no solution, one solution, or infinitelymany solutions. Answer: Since the graphs of and are parallel, there are no solutions. Example 1a

  8. Use the graph to determine whether the system has no solution, one solution, or infinitelymany solutions. Answer: Since the graphs of and are intersecting lines, there is one solution. Example 1b

  9. Use the graph to determine whether the system has no solution, one solution, or infinitelymany solutions. Answer: Since the graphs of and coincide, there are infinitely many solutions. Example 1c

  10. Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitelymany solutions. If the system has one solution, name it. Answer: Example 2a The graphs of the equations coincide. There are infinitely many solutions of this system of equations.

  11. Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitelymany solutions. If the system has one solution, name it. Answer: Example 2b The graphs of the equations are parallel lines. Since they do not intersect, there are no solutions of this system of equations.

  12. Variables Let the number of hours they rode and the number of hours they walked. Write a system of equations to represent the situation. Example 3 Bicycling Tyler and Pearl went on a 20-kilometer bike ride that lasted 3 hours. Because there were many steep hills on the bike ride, they had to walk for most of the trip. Their walking speed was 4 kilometers per hour. Their riding speed was 12 kilometers per hour. How much time did they spend walking? Words You have information about the amount of time spent riding and walking. You also know the rates and the total distance traveled.

  13. The number ofhours riding the number ofhours walking the total number of hours of the trip. plus equals r + w = 3 The distancetraveled riding the distancetraveled walking the total distance of the trip. plus equals 12r + 4w = 20 Example 3 cont Equations

  14. Graph the equations and . Example 3 cont The graphs appear to intersect at the point with the coordinates (1, 2). Check this estimate by replacing r with 1 and w with 2 in each equation. Answer: Tyler and Pearl walked for 3 hours.

  15. Summary & Homework • Summary: • Homework: • Pg 372 16-36 even

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