Linear Combination of Vectors simple problem So I've embarked on teaching myself Linear Algebra with G. Hadley's book which I found in my mom's library. The first chapter teacher vectors, linear dependence, and define subspaces and bases but I can't solve this simple problem in the problems section:
Express x=[4,5] as a linear combination of a=[1,3], b=[2,2].
So by my understanding this is asking what scalars can you multiply these vectors by and then add them so you get [4,5] as a solution. But it seems to me logically that no matter how you manipulate these values you can't get the difference between them to be only 1, since [1,3] has a difference of 2 and [2,2] just scales both values up equally. I'm sure I'm missing something simple and fundamental. Thanks for any help!

Solve the linear system
$$\begin{cases}x\;\,+2y=4\\3x+2y=5\end{cases}$$
and you'll find the coefficients $\;x,y\;$ that give you the linear combination. As observed in the comments, these coefficients do not have to be integers, and also check the above system has a unique solution (why?)
