1. Over Lesson 8–9 A.A B.B C.C D.D 5-Minute Check 1 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? A.y = 3x + 15 B.y = x + 5 C.y = 3x – 15 D. Use the line of best fit from above to predict the number of visitors in 2010.

2. Splash Screen

3. Then/Now 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.

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

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

6. Example 1 Solve by Graphing Answer: The solution of the system is (1, 3). The graphs appear to intersect at (1, 3). Check this by replacing x with 1 and y with 3. Check y=–x + 4y=2x + 1 3=33=33=33=3 3=–1 + 43=2(1) + 1 ??

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

8. Example 2A 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=4xMark downloaded 4 times as many songs as Catori. y=x + 6Mark downloaded 6 more songs than Catori. Answer:y = 4x and y = x + 6

9. Example 2B 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.

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

11. A.A B.B C.C D.D Example 2 CYP B 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. B. Andy ran twice as far as Ron and Andy ran 8 miles farther than Ron. How far did each person run?

12. Example 3A No Solution and Infinitely Many Solutions A. Solve the system of equations by graphing. y = –x – 3 2x + 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.

13. Example 3B No Solution and Infinitely Many Solutions B. Solve the system of equations by graphing. y = 2x y = 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.

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

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

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

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

18. Concept

19. End of the Lesson