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Over Lesson 8–9 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. A. B. C. D. A B C D 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. • system of equations A set of two or more equations with the same variables • substitution Use algebraic methods to find an exact solution of a system of equations. Solve by Graphing Solve the system of equations by graphing. y = –x + 4 y = 2x + 1 Graph each line. 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 ? 3 = –1 + 4 3 = 3 y = 2x + 1 ? 3 = 2(1) + 1 3 = 3 Answer: The solution of the system is (1, 3). What is the solution of the system of equations? y = –x + 3 y = 4x – 2 A. (2, 1) B. (2, –1) C. (1, 2) D. (1, –2) A. B. C. D. A B C D 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 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. 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 = 2x y=x–8 B. y = 8x y=x–2 C. y = 2x y=x+8 D. y = 8x y=x+2 A. B. C. D. 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. A. B. C. D. A B C D 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. 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. A. Solve the system of equations by graphing. y=x+1 2y – 2x = 2 A. (0, 1) B. (1, 2) C. infinitely many solutions D. no solution A. B. C. D. A B C D B. Solve the system of equations by graphing. y=x y=x+1 A. (1, 1) B. (1, 2) C. infinitely many solutions D. no solution A. B. C. D. A B C D 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 – 5 Write the second equation. 7 = 2x – 5 Replace y with 7. 12 = 2x 6=x Add 5 to each side. Solve for x. Answer: The solution of this system of equations is (6, 7). Solve the system of equations by substitution. y=8 y=x+4 A. (4, 8) B. (–4, 0) C. (8, 4) D. (2, 8) A. B. C. D. A B C D