Algebra 1 Notes

Lesson 7-1

Graphing Systems of Equations

Mathematics Standards- Patterns, Functions and Algebra: Generalize

patterns using functions or relationships, and freely translate among tabular, graphical and symbolic representations.

- Patterns, Functions and Algebra: Describe problem situations by using tabular, graphical, and symbolic representations.

- Patterns, Functions and Algebra: Demonstrate the relationship among zeros of a function, roots of equations and solutions of equations graphically and in words.

Mathematics Standards- Patterns, Functions and Algebra: Solve real-

world problems that can be modeled using linear, quadratic, exponential or square root functions.

- Patterns, Functions and Algebra: Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology.

- Patterns, Functions and Algebra: Solve real-world problems that can be modeled using systems of linear equations and inequalities.

Vocabulary

System of Equations – Two or more equations together

Ex/ 2x + 3y = 5

y = -4x + 6

Solution to Systems – Ordered pair that makes both equation true

Three possibilities

Vocabulary

System of Equations – Two or more equations together

1)Exactly one solution – equations make intersecting lines

Vocabulary

System of Equations – Two or more equations together

1)Exactly one solution – equations make intersecting lines

The one solution is

where the lines intersection. (x,y)

Vocabulary

System of Equations – Two or more equations together

2) Infinitely many solutions – equations make the same line

Vocabulary

System of Equations – Two or more equations together

2) Infinitely many solutions – equations make the same line

“Infinitely many solutions”

Vocabulary

System of Equations – Two or more equations together

3) No solutions – equations make lines that DON’T intersect (parallel)

Vocabulary

System of Equations – Two or more equations together

3) No solutions – equations make lines that DON’T intersect (parallel)

“No solutions”

Work the next two examples on your own paper

Example 1

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.

y = -x + 8

y = 4x - 7

Example 1

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.

y = -x + 8

y = 4x - 7

Example 1

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.

y = -x + 8

y = 4x - 7

Example 1

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.

y = -x + 8

y = 4x - 7

Example 1

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.

y = -x + 8

y = 4x - 7

Example 1

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.

y = -x + 8

y = 4x - 7

Example 1

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.

y = -x + 8

y = 4x - 7

Example 1

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.

y = -x + 8

y = 4x – 7

Find the point of

intersection

Example 1

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.

y = -x + 8

y = 4x – 7

Find the point of

intersection

Example 1

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.

y = -x + 8

y = 4x – 7

Find the point of

Intersection (3,5)

Example 2

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.

x – 2y = 4

x – 2y = -2

Example 2

x – 2y = 4 x – 2y = -2

– x – x

-2y = 4 – x

-2 -2

y = -2 + ½x

y = ½x – 2

Example 2

x – 2y = 4 x – 2y = -2

– x – x – x – x

-2y = 4 – x

-2 -2

y = -2 + ½x

y = ½x – 2

Example 2

x – 2y = 4 x – 2y = -2

– x – x – x – x

-2y = 4 – x -2y = -2 – x

-2 -2

y = -2 + ½x

y = ½x – 2

Example 2

x – 2y = 4 x – 2y = -2

– x – x – x – x

-2y = 4 – x -2y = -2 – x

-2 -2 -2 -2

y = -2 + ½x

y = ½x – 2

Example 2

x – 2y = 4 x – 2y = -2

– x – x – x – x

-2y = 4 – x -2y = -2 – x

-2 -2 -2 -2

y = -2 + ½x y = 1 + ½x

y = ½x – 2

Example 2

x – 2y = 4 x – 2y = -2

– x – x – x – x

-2y = 4 – x -2y = -2 – x

-2 -2 -2 -2

y = -2 + ½x y = 1 + ½x

y = ½x – 2 y = ½x + 1

Example 2

y = ½x – 2 y = ½x + 1

No Solution

Now go back to the guided notes

Story ProblemMr. Clem went on a 20 mile “bike-hike” that lasted 3 hours. His hiking speed was 4 mph, and his riding speed was 12mph. How long did he walk? How long did he ride?

X –

Y -

Story ProblemMr. Clem went on a 20 mile “bike-hike” that lasted 3 hours. His hiking speed was 4 mph, and his riding speed was 12mph. How long did he walk? How long did he ride?

X – ride time

Y -

Story ProblemMr. Clem went on a 20 mile “bike-hike” that lasted 3 hours. His hiking speed was 4 mph, and his riding speed was 12mph. How long did he walk? How long did he ride?

X – ride time

Y - walk time

x + y = 3

12x + 4y = 20

Story Problemx + y = 3 12x + 4y = 20

– x – x

y = -x + 3

Story Problemx + y = 3 12x + 4y = 20

– x – x – 12x – 12x

y = -x + 3

Story Problemx + y = 3 12x + 4y = 20

– x – x – 12x – 12x

y = -x + 3 4y = -12x + 20

Story Problemx + y = 3 12x + 4y = 20

– x – x – 12x – 12x

y = -x + 3 4y = -12x + 20

4 4

y = -3x + 5

Story Problemy = -x + 3 y = -3x + 5

x = hoursrode

y = hours

walked

They walked for 2 hours.

They rode for 1 hour.

(1, 2)

Homework

Pgs. 372

16-40 (evens) 41-45 (all)