Been working on this problem for nearly 45 minutes now, totally confused.

4.5x - 6.7y = 8.6
3.8x +2.2 = y

well, you know that

y = 3.8x+2.2

so use that in the other equation to get

4.5x - 6.7(3.8x+2.2) = 8.6
4.6x - 25.46x - 14.74 = 8.6

now it's easy, right?
Then, once you have x, use that to get y.