Linear transformation

Given that a linear transformation moves points (1,0) and (2,-3) to (2,-1) and (1,3), respectively, determine the image of point (-3,6).

I don't get the first step to the solution.

[Sol] Letting (-3,6) =k(1,0)+L(2,-3)

k=1, L=-2

How do you know what k and L is?

Never mind, I got it. Simultaneous equations.

Actually I still need help.

I don't get the last step, how do you get (0,-7)?

http://i25.tinypic.com/2py15b8.jpg

I found out again (it was so simple)

They tell you what f(1,0) and f(2,-3) is.