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### 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.

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

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

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

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. 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 system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.

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

o system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.

f

s + f = 24

3s + f = 44

(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

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