Hint:
Substitute for y in the first equation:
x=ln(3+ln(x)), an equation involving only one variable. The log of a number is always smaller than the number itself so this fact can be used to generate an iterative process. Start with x=1; the next value for x becomes ln(3)=1.1 approx; the next value of x is ln(3+ln(1.1))=1.13; the next value is ln(3+ln(1.13))=1.14; the next 1.141 and so on. With each iteration the result converges fairly rapidly to a stable approximation to 4 decimal places. At that point y can be found from the second equation. Using a calculator more accuracy is obtained than the figures given above as examples, and a solution is forthcoming when the accuracy of the calculator is reached so that no new values are generated (1.141890548916, for example, y=1.632685265061).