So I'm trying to solve this partially decoupled system:

1.) Solve it WITHOUT using matrices. (HINT: start with the second equation)

2.) Solve it with using matrices.

I can do #2... but #1 is so hard.

For #2, I set up the system into a matrix so I get X' = AX, with A being:

[[2,3],[0,-4]]

Then, I found the eigenvalues:

And the corresponding eigenvectors (call them , respectively:

k_1 = [[1],[0]], k_2 = [[1/2],[1]

So then the solution is:

Voila.

Now for #1...

So solving the 2nd equation first...:

Solve for y (I ignored the absolute value so I don't get 2 diff soln's):

So now plug this into 1st eq.:

No idea how to solve this! Maybe I did something wrong.. no idea.