Let's solve the equation by substitution.

From the first equation, we can express 3^x in terms of 3^y by rearranging the equation:

3^x = 6 + 3^y

Now, substitute this expression into the second equation:

2(6 + 3^y) + 3^y = 21
12 + 2(3^y) + 3^y = 21
12 + 6^y + 3^y = 21

Combining like terms:
9 + 9^y = 21

Subtract 9 from both sides:
9^y = 12

Taking the logarithm of both sides to solve for y:
log(9^y) = log(12)
y = log(12)/log(9)

y ≈ 1.2618

Now, plug the value of y back into the first equation to solve for x:

3^x = 6 + 3^(1.2618)
3^x = 6 + 3^1.2618
3^x ≈ 9.3492

Taking the logarithm of both sides to solve for x:
x = log(9.3492)/log(3)
x ≈ 2.0232

Therefore, the solution to the system of equations is x ≈ 2.0232 and y ≈ 1.2618.