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You graphed linear equations. Determine the number of solutions a system of linear equations has. Solve systems of linear equations by graphing. Then/Now

Concept

Number of Solutions A. Use the graph to determine whether the system is consistent or inconsistent and if it is independent or dependent. y = –x + 1 y = –x + 4 Answer: The graphs are parallel, so there is no solution. The system is inconsistent. Example 1A

Number of Solutions B. Use the graph to determine whether the system is consistent or inconsistent and if it is independent or dependent. y = x – 3 y = –x + 1 Answer: The graphs intersect at one point, so there is exactly one solution. The system is consistent and independent. Example 1B

A. Use the graph to determine whether the system is consistent or inconsistent and if it is independent or dependent. 2y + 3x = 6 y = x – 1 A. independent B. inconsistent C. dependent D. cannot be determined 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Example 1A

B. Use the graph to determine whether the system is consistent or inconsistent and if it is independent or dependent. y = x + 4 y = x – 1 A. independent B. inconsistent C. dependent D. cannot be determined 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Example 1B

Solve by Graphing A. Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it. y = 2x + 3 8x – 4y = –12 Answer: The graphs coincide. There are infinitely many solutions of this system of equations. Example 2A

Solve by Graphing B. Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it. x – 2y = 4 x – 2y = –2 Answer: The graphs are parallel lines. Since they do not intersect, there are no solutions of this system of equations. Example 2B

A. Graph the system of equations A. Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it. A. one; (0, 3) B. no solution C. infinitely many D. one; (3, 3) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Example 2A

B. Graph the system of equations B. Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it. x + 3y = 4 1/3 x + y = 0 A. one; (0, 0) B. no solution C. infinitely many D. one; (1, 3) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Example 2B

Write and Solve a System of Equations BICYCLING Naresh rode 20 miles last week and plans to ride 35 miles per week. Diego rode 50 miles last week and plans to ride 25 miles per week. Predict the week in which Naresh and Diego will have ridden the same number of miles. Example 3

Write and Solve a System of Equations Example 3

Graph the equations y = 35x + 20 and y = 25x + 50. Write and Solve a System of Equations Graph the equations y = 35x + 20 and y = 25x + 50. The graphs appear to intersect at the point with the coordinates (3, 125). Check this estimate by replacing x with 3 and y with 125 in each equation. Example 3

Check y = 35x + 20 y = 25x + 50 125 = 35(3) + 20 125 = 25(3) + 50 Write and Solve a System of Equations Check y = 35x + 20 y = 25x + 50 125 = 35(3) + 20 125 = 25(3) + 50 125 = 125 125 = 125   Answer: The solution means that in week 3, Naresh and Diego will have ridden the same number of miles, 125. Example 3

A. 225 weeks B. 7 weeks C. 5 weeks D. 20 weeks Alex and Amber are both saving money for a summer vacation. Alex has already saved $100 and plans to save $25 per week until the trip. Amber has $75 and plans to save $30 per week. In how many weeks will Alex and Amber have the same amount of money? A. 225 weeks B. 7 weeks C. 5 weeks D. 20 weeks 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Example 3

Assignment Page 338 Problems 2 – 24 (evens) Due Friday