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5-Minute Check 1

A B C D. A. y = 3 x + 15 B. y = x + 5 C. y = 3 x – 15 D. Which is an equation for the line of best fit for the scatter plot where x is the years since 1998 and y is the number of visitors in thousands?.

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5-Minute Check 1

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  1. A B C D A.y = 3x + 15 B.y = x + 5 C.y = 3x – 15 D. Which is an equation for the line of best fit for the scatter plot where x is the years since 1998 and y is the number of visitors in thousands? Use the line of best fit from above to predict the number of visitors in 2010. 5-Minute Check 1

  2. Splash Screen

  3. You have already solved linear equations by graphing. (Lesson 8–2) • Solve systems of linear equations by graphing. • Solve systems of linear equations by substitution. Then/Now

  4. A set of two or more equations with the same variables • system of equations • substitution Use algebraic methods to find an exact solution of a system of equations. Vocabulary

  5. Solve by Graphing Solve the system of equations by graphing. y = –x + 4y = 2x + 1 Graph each line. Example 1

  6. ? ? 3 = –1 + 4 3 = 2(1) + 1 Solve by Graphing The graphs appear to intersect at (1, 3). Check this by replacing x with 1 and y with 3. Check y = –x + 4 y = 2x + 1   3 = 3 3 = 3 Answer: The solution of the system is (1, 3). Example 1

  7. A B C D What is the solution of the system of equations?y = –x + 3y = 4x – 2 A. (2, 1) B. (2, –1) C. (1, 2) D. (1, –2) Example 1

  8. A. Catori and Mark each download songs. Mark downloaded 4 times as many songs as Catori. Mark also downloaded 6 more songs than Catori. Write a system of equations to represent this situation. Let x represent Catori’s songs and y represent Mark’s songs. y = 4x Mark downloaded 4 times as many songs as Catori. y = x + 6 Mark downloaded 6 more songs than Catori. Answer: y = 4x and y = x + 6 Example 2A

  9. B. Catori and Mark each download songs. Mark downloaded 4 times as many songs as Catori. Mark also downloaded 6 more songs than Catori. Solve the system by graphing. Explain what the solution means. Graph the equations y = 4x and y = x + 6 on the same coordinate grid. The equations intersect at (2, 8). Answer: So, the solution to the system is x = 2 and y = 8. This means that Catori downloaded 2 songs and Mark downloaded 8 songs. Example 2B

  10. A B C D A. Andy ran twice as far as Ron and Andy ran 8 miles farther than Ron. Which system of equations represents this situation? A.y = 2xy = x – 8 B. y = 8xy = x – 2 C. y = 2xy = x + 8 D. y = 8xy = x + 2 Example 2 CYP A

  11. A B C D B. Andy ran twice as far as Ron and Andy ran 8 miles farther than Ron. How far did each person run? A. Andy ran 10 miles.Ron ran 5 miles. B. Andy ran 12 miles.Ron ran 6 miles. C. Andy ran 16 miles.Ron ran 8 miles. D. Andy ran 18 miles.Ron ran 9 miles. Example 2 CYP B

  12. No Solution and Infinitely Many Solutions A. Solve the system of equations by graphing. y = –x – 32x + 2y = –6 Both equations have the same graph. Any ordered pair on the graph will satisfy both equations. Answer: Therefore, there are infinitely many solutions of this system of equations. Example 3A

  13. No Solution and Infinitely Many Solutions B. Solve the system of equations by graphing. y = 2xy = 2x – 4 The graphs appear to be parallel lines. Answer: Since there is no coordinate pair that is a solution to both equations, there is no solution of this system of equations. Example 3B

  14. A B C D A. Solve the system of equations by graphing.y = x + 12y – 2x = 2 A. (0, 1) B. (1, 2) C. infinitely many solutions D. no solution Example 3A

  15. A B C D B. Solve the system of equations by graphing.y = xy = x + 1 A. (1, 1) B. (1, 2) C. infinitely many solutions D. no solution Example 3B

  16. Solve by Substitution Solve the system of equations by substitution. y = 7y = 2x – 5 Replace y with 7 in the second equation. y = 2x – 5 Write the second equation. 7 = 2x – 5 Replace y with 7. 12 = 2x Add 5 to each side. 6 = x Solve for x. Answer: The solution of this system of equations is (6, 7). Example 4

  17. A B C D Solve the system of equations by substitution. y = 8y = x + 4 A. (4, 8) B. (–4, 0) C. (8, 4) D. (2, 8) Example 4

  18. Concept

  19. End of the Lesson

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