Graphing Systems of Equations 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. 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.

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

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 O x y y = x - 3 B. y = -x + 5 2x + 2y = -8 y = -x -4 2x + 2y = -8 y = -x - 4 2x + 2y = -8

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

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

Graph each system of equations 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

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

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

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