Qualification > Math

IB HELP: Patterns within systems of linear equations

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Reemay:
First of all, Hello- I'm new to the site =)
I have a few questions which I need some help on. Any advice/suggestions would be very helpful.

1. Consider the 2x2 system of linear equations=
x+2y=3
2x-y=-4

- Examine the constants in the first equation and describe any patterns. Repeat for the second equation
Where I am up to:
1st equation- 1, 2, 3 (+1)
2nd equation- 2, -1, -4 (-3)
How do I describe the patterns?

- Solve the above system. Display your solution graphically. What is the significance of the solution?
I am assuming that solving the equation means finding out x and - so this can be done through matrices or simultaneous equations right? Well, I've gone for the matrices method and it worked it! I ended up with x=-1,y=2.. And I'm done with the graph, as well, showing the intersection at (-1, 2)... WHAT'S THE SIGNIFICANCE??

- Create and solve a few more systems similar to the example above. Comment on your solutions
What exactly are similar solutions?


- Make a conjecture regarding this type of 2x2 system and prove it..

- Using technology, extend your investigation to 3x3 systems whose constants exhibit the same patterns seen above

- Make a conjecture regarding the solution to those 3x3 systems and prove your conjecture...

ANYBODY???

astarmathsandphysics:
I will answer this. 1st thing in morning

Reemay:
Thx.. U're a life saver  :)

Alpha:

--- Quote from: Reemay on August 21, 2010, 12:46:16 am ---
1. Consider the 2x2 system of linear equations=
x+2y=3
2x-y=-4

- Examine the constants in the first equation and describe any patterns. Repeat for the second equation
Where I am up to:
1st equation- 1, 2, 3 (+1)
2nd equation- 2, -1, -4 (-3)
How do I describe the patterns?


--- End quote ---

They are arithmetic progressions.


--- Quote ---- Solve the above system. Display your solution graphically. What is the significance of the solution?
I am assuming that solving the equation means finding out x and - so this can be done through matrices or simultaneous equations right? Well, I've gone for the matrices method and it worked it! I ended up with x=-1,y=2.. And I'm done with the graph, as well, showing the intersection at (-1, 2)... WHAT'S THE SIGNIFICANCE??
--- End quote ---

Solving means finding the point of intersection of these two lines, where they meet, their common point.

Is it what you were looking for?  :-\

Reemay:
I don't know! I've already drawn the graph and found the point of intersection... Not sure about the significance, though!

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