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

Fill in the Blanks

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.