What are variables x and y if 3^(x+y)-243=0 and x=6/y ?

We'll write 243 as a power of
3.

3^(x+y) - 3^5 = 0

We'll
move 3^5 to the right side:

3^(x+y) =
3^5

Since the bases are matching, we'll use one to one
property of exponentials:

x + y = 5
(1)

We'll multiply by y the second
equation:

x*y = 6*y/y

We'll
simplify and we'll get:

x*y = 6
(2)

To ease the work, we'll use the following terms instead
of the variables x and y:

x + y = S and x*y =
P.

S = 5 and P = 6

We'll
create the quadratic equation  with the sum and the product
above:

x^2 - Sx + P = 0

x^2 -
5x + 6 = 0

We'll apply the quadratic
formula:

x1 = [5+sqrt(25 -
24)]/2

x1 = (5 + 1)/2

x1 = 3
=> y1 = 5 - x1

y1 = 5 -
3

y1 = 2

x2 =
2

y2 = 5 - 2

y2 =
3

So, the variables x and y are represented
by the following pairs: {2; 3} and {3; 2}.