Author Topic: ib mathematics linear equations help??  (Read 2504 times)

Offline Gazelle

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ib mathematics linear equations help??
« on: August 25, 2010, 05:20:16 pm »
I have this 2x2 linear system:
x+2y=4
5x-y=1/5

The question is: set up and solve a general 2x2 system that incorporates
the pattern found above..


I came up with the general system but I'm stuck somewhere in solving
it..

What I'm up to:
I know that the pattern is geometric progression (The coefficients
increase or decrease by a common ratio)
So, i came up with a general system of:
ax + ary = ar^2
bx + bny = bn^2

And every time I try to solve it I end up with (Y = r+n) and (x= -rn),
I can't really solve it...
P.S: I've already solved the original system using Gauss elimination
and found x=2/5 and y=9/5...


thx

Offline Saladin

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Re: ib mathematics linear equations help??
« Reply #1 on: August 26, 2010, 11:50:01 am »
I will endeavor to answer this if time permits me.

Offline Saladin

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Re: ib mathematics linear equations help??
« Reply #2 on: August 26, 2010, 12:29:02 pm »
I have this 2x2 linear system:
x+2y=4
5x-y=1/5

The question is: set up and solve a general 2x2 system that incorporates
the pattern found above..


I came up with the general system but I'm stuck somewhere in solving
it..

What I'm up to:
I know that the pattern is geometric progression (The coefficients
increase or decrease by a common ratio)
So, i came up with a general system of:
ax + ary = ar^2
bx + bny = bn^2

And every time I try to solve it I end up with (Y = r+n) and (x= -rn),
I can't really solve it...
P.S: I've already solved the original system using Gauss elimination
and found x=2/5 and y=9/5...


thx

Solve the thing using simultaneous equations.

So, this is how you do it.

 5(x+2y=4)

 5x+10y=20

Now you simply replace to take away x from the equation.

 5x=20-10y
 
 y=\frac{9}{5}

 x=\frac{2}{5}

So, I can approve of your answers, but I have not heard of this method before. I think Dibbs will be better acquainted with it than I am.