Y = x + 2 and y=3x-4 solved using substitution

So I did this:

y=x + 2

y=3x-4

I used the first equation to plug into the second equation.

x+2 = 3x - 4

I subtracted 3 from both sides so I get

-2x+2=-4

So I subtract 2 from both sides so I get

-2x=-6

I divide - 2 on both sides and so I get

x=3

Then I plug the x into either equation. I did the first equation.

y=3+2

y=5

So x=3 and y=5