Vector - sum of two vectors * some const

[asdfmaster]

a*<3, 2> + b*<-2, 3> = <2, 3> - A, B?

Homework Statement

There exists a vector <2, 3>.
Said vector is the sum of two other vectors <3, 2> and the orthoginal to <3,2> (which I think is <-2, 3> right?)

Homework Equations

<2, 3> = a<3, 2> + b<-2, 3> where a, b are constants

The Attempt at a Solution

I tried solving the x and y seperately: 2 = a*3 + b*-2 but there's many ways this can be done, none of which held true also for the y.

 

[asdfmaster]

Maybe I didn't describe it well enough. The problem is that I have a vector <2, 3> and I must get from the origin to (2, 3). I start moving parallel to <3, 2> and make a right angle turn. Where do I make the right angle turn?

 

[foxjwill]

EDIT:
I take back the above matrix, which I am now deleting. The system you'll need to solve is

$$\begin{align*} 2x + 3y &= 13\\ 2x - 3y &= 0 \end{align*}$$

Which can be solved via elimination.

 

[asdfmaster]

Well, I just tried elimination using gaussian elimination

Starting matrix:
2  3    13
2 -3    0

to
2  3    13
0 -6   13

to
1  3/2    13/2
0  1      13/-6

to
1  0    39/4
0  1    13/-6

so I end up with x = 39/4 and y=13/-6
But I asked and he told me that it wasn't correct.

 

[foxjwill]

Well, I just tried elimination using gaussian elimination

Starting matrix:
2  3    13
2 -3    0

to
2  3    13
0 -6   13

to
1  3/2    13/2
0  1      13/-6

to
1  0    39/4
0  1    13/-6

so I end up with x = 39/4 and y=13/-6
But I asked and he told me that it wasn't correct.

Has he given you the correct answer? Maybe I don't understand the question completely.