Systems of Linear Equations: Graphing

Solving Systems of Linear Equations: Graphing

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Then answer Chat Question of the Day.

​Lesson Essential Question:
How does one solve real-world problems by graphing systems of linear equations?

​Chat Question of the Day:
(Answer the following question in the private Zoom chat.)
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Graphing Review

How do you graph linear equations using slope-intercept and standard form?

Graphing

Graph a line that represents the following situation:

Erika has a 1 meter head start and rides her bike at a constant rate of 2 meters for every 3 seconds.

Graphing

Graph the equation: $$y\ =\ -\frac{1}{3}x+2$$

Multiple Select

Why do we draw a line through plotted points of a linear equation?

(Select all that apply.)

• To visually represent the relationship between the variables
• To hide the true relationship between the variables
• To represent all of the infinite points that make the equation true

• To demonstrate variables come before numbers

Draw

Read the following situation:

Your friend's family decides to rent a room on AirBnB. They spend $600 preparing a bedroom to rent. The cost for your friend's family for utilities and supplies is $15 per night. They charge $75 a night to rent the bedroom.

Definition: A system of linear equations, also known as a linear system, consists of two or more linear equations with the same variables.

For example, the two equations we wrote from the previous slide is a system of linear equations:

Total Cost to Rent: y = 15x + 600 
Revenue (income): y = 75x

Graphing Linear Systems

Costs: ​ y = 15x + 600
 Revenue (income): y = 75x

Open Ended

Do you notice anything that happens when we graph both lines?

Definition: A solution to a system of linear equations is an ordered pair (x, y) that makes both equations true. When we graph a linear system, the point of intersection is the solution.

(2, 5)
y = - x + 7
5 = - 2 + 7
5 = 5
True

(2, 5)
y = 2x + 1
5 = 2 (2) + 1
5 = 4 + 1
True

Multiple Choice

What is the solution to this linear system?

y = 15x + 600

y = 75x

• The solution is x = 10 & y = 750.

  (10, 750)

• The solution is x = 750 & y = 10.

  (750, 10)

• The solution is x = 0 & y = 600.

  (0, 600)

Draw

How do you know (10, 750) is the solution to the linear system below?

y = 15x + 600

y = 75x

(Show your work.)

Drag and Drop

Recall the situation: "Your friend's family decides to rent a room on AirBnB. They spend $600 preparing a bedroom to rent. The cost for your friend's family for utilities and supplies is $15 per night. They charge $75 a night to rent the bedroom." and we found the solution to be (10, 750).
This means: After ​

Placeholder

nights, the cost of renting a bedroom and the revenue (income) will be the same at ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

10

$750

750

$740

$10

20

RECAP:
What have you learned?

Multiple Choice

What is the solution to a graphed linear system?

• the y-intercept

• the x-intercept

• the point of intersection

Multiple Choice

What is the solution the linear system?

• (-2, 1)

• (-1, 2)

• (2, -1)

• (1, -2)

Multiple Choice

What is the solution to the system?

• (3, -1)
• (2, -6)
• No Solution 
• (6, -2)

Multiple Choice

Is (-2, 3) the solution to the linear system: y = 3x + 9 and 2x + y = - 8 ?

• No

• Yes

Poll

How do you feel about the lesson?

• I could teach this to someone else!

• I got it!

• Engaged, but I need a little more practice.

• I was distracted today. Will you review this with me again?

Word Cloud

How should we review in our next game day?