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Types of Solutions to Simultaneous Linear Equations

Author:Sanjay Bhatt, Shelby Povlick, Ibu Krisna
Topic:Algebra

Description:

Above you see two linear equations graphed on the same coordinate plane. You have been learning about how to graph systems of equations in order to find their solutions. During the next 3 Investigations, you will discover the different types of solutions there are to systems of linear equations and explore how the differences can be seen between them by looking at the graph and equations. Both equations are written in slope-intercept form where The blue equation corresponds with the blue line. This equation will not change during your investigations. The red equation corresponds with the red line. By manipulating the sliders (that are also red), you will be able to change the equation and make conjectures about the different types of solutions to systems of linear equations.

Question 1

1. Drag slider m to change the slope of the red line to different values (except for m=3). 2. Keeping that slider the same, drag the b slider to change the y-intercept of the red line to various values.

How many points of intersection are there?

Question 2

1. Drag slider m to change the slope of the red line to m=3. 2. Keeping that slider the same, drag the b slider to change the y-intercept of the red line to various values (except b=2)

How many points of intersection are there?

Question 3

1. Drag slider m to change the slope of the red line to m=3. 2. Keeping that slider the same, drag the b slider to change the y-intercept of the red line to b=2.

How many points of intersection are there?

Question 4

Is there any relation between the pair of equations in each question above? Justify why your rule works using mathematical reasoning. You may refer to the properties of lines, slopes, and intercepts.

How many points of intersection are there?

Question 5:

What type of solution would the following system of equations have? Choose your answer and then on your Investigation Sheet, explain how you know without graphing the system.

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Question 6:

What type of solution would the following system of equations have? Choose your answer and then on your Investigation Sheet, explain how you know without graphing the system.

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Question 7:

What type of solution would the following system of equations have? Choose your answer and then on your Investigation Sheet, explain how you know without graphing the system.

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Question 8:

What type of solution would the following system of equations have? Choose your answer and then on your Investigation Sheet, explain how you know without graphing the system.

Select all that apply
  • A
  • B
  • C
Check my answer (3)

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