Types of Solutions to Simultaneous Linear Equations
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
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)
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.
Question 4:
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.
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.
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.
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.