The second equation gives you an expression for y that can be substituted into the first equation.
... 2x + 2(x+3) = 38 . . . . . x+3 substituted for y
... 2x +2x +6 = 38 . . . . . eliminate parentheses
... 4x = 32 . . . . . . . . . . . subtract 6
... x = 8 . . . . . . . . . . . . . . divide by 4
... y = 8 + 3 = 11 . . . . . . . use the second equation to find y
The solution to the system is (x, y) = (8, 11).