6.1 Solving Linear Systems by Graphing

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6.1 Solving Linear Systems by Graphing. Standard: SWBAT solve a system of two linear equations in two variables and are able to interpret the answer graphically. http://apod.nasa.gov/apod/ap081212.html. Lick Observatory Moonrise. Mini Quiz 48. Is the ordered pair a solution to the equation

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### 6.1 Solving Linear Systems by Graphing

Standard: SWBAT solve a system of two linear equations in two variables

and are able to interpret the answer graphically.

http://apod.nasa.gov/apod/ap081212.html

Lick Observatory Moonrise

Mini Quiz 48

Is the ordered pair a solution to the equation

2x – 3y = 5

• (1, 0)
• (4, 1)
• Graph the line 2x – y + 3 = 0
Overview
• Solving Systems of Linear Equations (two equations) by Graphing
• Understanding No Solution
• Understanding Infinite Solution
Graphing Lines Quick Review

What are the different ways to graph a line?

• T-chart
• Slope-Intercept Form: y = mx + b
• x- and y-intercepts: Using Standard Form:

Ax + By = C

Graph the line x – 2y – 4 = 0

Graphing Systems of Linear Equations

Step:

• Graph each line on the same coordinate plane
• Label the point (ordered pair) where the lines cross (intersect)
Graphing Lines

Solve the Systems by Graphing

1.

Check: (1, 2)

y = 3x – 1

2 = 3(1) – 1

2 = 3 – 1

2 = 2 

y = -2x + 4

2 = -2(1) + 4

2 = -2 + 4

2 = 2 

Where do the lines cross?

(1, 2)

Graphing Lines

Solve the Systems by Graphing

2.

Check: (1, -3)

y = 4x – 7

-3 = 4(1) – 7

-3 = 4 – 7

-3 = -3 

Where do the lines cross?

(1, -3)

y = -3x

-3 = -3(1)

-3 = -3 

Graphing Lines

Solve the Systems by Graphing

3.

Check: (-1, 5)

y = 2x + 7

5 = 2(-1) + 7

5 = -2 + 7

5 = 5 

y = x + 6

5 = (-1) + 6

5 = 5 

Where do the lines cross?

(-1, 5)

Special Cases – No Solution and Infinitely Many Solutions

No SolutionsInfinitely Many Solutions

4. 6.

5. 7.

Solve for y and look at the equations, what do you notice about the equations?

Same slope

Different y-intercept

Same slope

Same y-intercept

Graphing Lines

Solve the Systems by Graphing

8.

x-intercept (x, 0)

3x = 12

x = 4

y-intercept (0, y)

3y = 12

y = 4

(4, 0)

Where do the lines cross?

No Solution

(0, 4)

Graphing Lines

Solve the Systems by Graphing

9.

Where do the lines cross?

Infinitely Many Solutions

x-intercept (x, 0)

3x = -3

x = -1

y-intercept (0, y)

y = -3

(-1, 0)

(-1, 0)

(0, -3)

Graphing Lines

Solve the Systems by Graphing

10.

Slope-intercept form

2x + y = 0

y = -2x

Where do the lines cross?

No Solution

Application

11. Suppose you have \$20 in your bank account. You start saving \$5 each week. Your friend has \$15 in her account and is saving \$10 each week. When will you and your friend have the same amount of money in your account?

y = 5x + 20

y = 10x + 5

After 3 weeks!

35

30

25

20

15

10

5

Amount Saved

1 2 3 4 5 6

Number of Weeks

Wrap Up
• Solving Linear System by Graphing
• Graph each line
• Find where they cross
• Check solution

HW: P. 279 #13-23 odd, P. 281 #43-51 odd

DLUQ: When graphing a linear system, where do you find the solution?