Graphing Systems Lesson Slides: 15 Slides

15 Slides • 4 Questions

1

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2

Intro to Systems

November 10

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" Jules opened a checking account with $500 and plans to spend $50 each week. Astrid opened a checking account with $50 and plans to save $25 each week. An equation is showing the relationship between x, the number of weeks and y, the account balance is shown for each account below.

4

Poll

Think About It:

Do you think Jules and Astrid can have the same amount of money in their bank accounts at some point?

(Discuss with your group your answer)

YES

NO

5

Where do the graphed lines intersect?

6

Open Ended

In your own words,

what does the point of intersection represent in the context of the situation?

(Hint: What does the x and y stand for in the word problem?)

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c. Prove that the point of intersection is a solution to each equation by substituting the values into the equations.

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*System of Equations: Two or more linear equations that use the same ____________ forms a system of equations.

*Solution of a System: The solution to a system of linear equations is the _______________ ________ that makes all the equations of the system true.

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______ solution:

_____ solution:

___________ solution:

Lines have different ________ and intersect at ______ point.

Lines have same ________ and different y-intercepts; do not intersect

Lines have same ________ and same y-intercept.

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Where do the graphed lines intersect?

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12

Where do the graphed lines intersect?

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14

Where do the graphed lines intersect?

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16

Where do the graphed lines intersect?

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18

Fill in the Blanks

Jack is choosing between two pest control companies.

Mouse Arrest: $y\ =\ 25x\ +\ 125$

Hugs Not Bugs: $y\ =\ 50x$

What is the solution to the system?

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19

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