8.4. Lesson 24- Intro to Simultaneous Equations

8.4. Lesson 24 & 25- Intro to Simultaneous Equations

Multiple Choice

Opener: A solution to a system would be the ordered pair that satisfies BOTH equations. Knowing this, answer yes or no.

• yes

• no

Fill in the Blanks

Write an equation to describe this data

Fill in the Blanks

Write an equation to describe this data

Multiple Choice

3. Which pair of numbers from your table in Exercise 2 would show Derek’s actual score of 30 points?

• (6,1)

• (7,2)

• (8,3)

• (9,4)

• 1(0,5)

Discussion (5 minutes)

• There are situations where we need to work with two linear equations simultaneously. Hence, the phrase simultaneous linear equations. Sometimes a pair of linear equations is referred to as a system of linear equations. 

• The situation with Derek can be represented as a system of linear equations. (show on board)

• We are looking for the ordered pair (𝑥, 𝑦) that makes both equations true. That point is called the solution to the system. 

• Systems of equations can have exactly one solution, no solution, or infinitely many solutions. This is a topic for later lessons.

Discussion Contd..

• Our goal is to determine the exact location on the coordinate plane where the graphs of the two linear equations intersect, ---that is the solution (x,y) that we are looking for!

Multiple Choice

The population growth of two towns over a period of five years is represented by the system of equations below, both algebraically and graphically.

​y=x+6

y=2x+2

Which ordered pair is the solution to the system of equations?​

• (2,6)

• (4,10)

• (6,2)

• (10,4)

Multiple Choice

• Yes

• No

Multiple Choice

• a

• b

• c

• d

Multiple Choice

• a

• b

• c

• d

Multiple Choice

• true

• false

Multiple Choice

Aiden and Noah are going to work for their neighbor this summer. The neighbor gives Aiden $ 25 at the beginning of the summer and then pays him $5 each week to mow the lawn. The neighbor pays Noah $ 7.50 each week to walk the dog. The graph shown below models the total amount of money y each boy has earned after working for x weeks

​What does the point of intersection on the graph represent?

• After 75 weeks, each boy has earned a total of $10

• After 10 weeks, each boy has earned $75

• After 10 weeks, Noah has earned a total of $75 and Aiden has earned a total of $10

• After 75 weeks, Noah has earned a total of $10 and Aiden has earned a total of $75

Open Ended

What are simultaneous or systems of equations?

Poll

Outcome Review

• I completely understand what a simultaneous equation is and I completely understand what a solution to a system of equations looks like.

• I kinda understand what a simultaneous equation is and I kinda understand what a solution to a system of equations looks like.

• I have no idea what a simultaneous equation is nor do I know what a solution to one looks like.