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Lesson 7-1

Lesson 7-1. Graphing Systems of Equations. Definition. Systems of Equations- Two equations together. A solution to a system of equations has 0, 1 or an infinite number of solutions. Consistent - If the graphs intersect or coincide, the system of equations is said to be consistent.

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Lesson 7-1

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  1. Lesson 7-1 Graphing Systems of Equations

  2. Definition • Systems of Equations- Two equations together. A solution to a system of equations has 0, 1 or an infinite number of solutions. • Consistent - If the graphs intersect or coincide, the system of equations is said to be consistent. • Inconsistent - If the graphs are parallel, the systems of equation is said to be inconsistent. • Consistent equations are independent or dependent. Equations with exactly one solution is independent. Equations with infinite solutions is dependent.

  3. y y y O O O x x x Intersecting Lines Same Line Parallel Lines Infinitely Many No solutions Exactly 1 solution Consistent and independent Consistent and dependent Inconsistent

  4. y O x Ex. 1 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. y = -x + 5 y = x -3 y = -x + 5 2x + 2y = -8 y = x - 3 B. y = -x + 5 2x + 2y = -8 y = -x -4 2x + 2y = -8 y = -x - 4 2x + 2y = -8

  5. y O x y = -x + 4 3x-3y=9 y = -x + 1 x - y = 3 Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions. y = -x + 1 y = -x + 4 b. 3x - 3y = 9 y = -x + 1 c. x - y = 3 3x - 3y = 9

  6. Ex. 2 Graph each 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 = -x + 8 y = 4x -7 B. x + 2y = 5 2x + 4y = 2 o y

  7. Graph each 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. 2x - y = -3 8x - 4y = -12 B. x - 2y = 4 x - 2y = -2 o y

  8. Write and Solve a System of Equations Ex. 3 If Guy Delage can swim 3 miles per hour for an extended period of time and the raft drifts about 1 mile per hour, how may hours did he swim each day if he traveled an average of 44 miles per day? Let s = the number of hours he swam and let f = the number of hours he floated each day. The number of hours swimming the number of hours floating equals hours in a day plus = s + f 24 total miles in a day The daily miles traveled the daily miles traveled floating equals plus = 3s + 1f 44

  9. o f s + f = 24 3s + f = 44 (10, 14) Guy spent about 10 hours swimming each day. s

  10. 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? (Hint: let r = number of hours riding and w = number of hours walking.) w r + w = 3 12 r + 4w = 20 They walked for 2 hours r

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