IB HELP: Patterns within systems of linear equations

[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]

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?

They are arithmetic progressions.

- 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??

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!

[Saladin]

These look like questions when they are first trying to explain the idea. Just do the questions in the book alter on, and if you have problems, iA, we will be here to help.

[astarmathsandphysics]

start here.By technology I assume is meant a TI *3 or similar. Is this for IB?

[Reemay]

O! Thx a mil! Thx for takin' the time.. It was really helpful =)