Solving applications: Systems of three Equations

I have this word problem that i am having trouble on i am usually good with word problems but my instructor has completely caught me off guard with this one:

The problem is:

The sum of three numbers is 85. The second is 7 more than the first. The third is 2 more than four times the second. Find the numbers.

So far what i have is:

Let x = the first number

let y = the second number

let z = the third number

x+y+z=85

y=2+x

Z=2+4y

This is where i am stuck. I have read the chapter multiple times and have yet to come up with the correct answer. Am i writing the correct equations for the problem given? If so, what step should i take about solving this? Please help thanks in advanced.