Missing solution - system of equations

Attention! This example already works as expected in Wolfram Mathematica 12.1.1.0 for function Solve.

The problem was in version 12.1.0.0. Check out answer of Bob Hanlon for more information here.

Original question

I am using Wolfram Mathematica 12.1.0.0. I want to solve a system of two equations. I want to get only real solutions.My questions are:

1. Where is the solution $(x,y)=(0,2)$?

2. How to get this solution?

f[x_, y_] := y + 2*4^(x + y - 1) - 10;g[x_, y_] := 4/(2*y - 3)^(1/2) + 2^(2 - x - y) - 5;Solve[{f[x, y] == 0, g[x, y] == 0}, {x, y}, Reals]

 {{x -> -(19/2), y -> 19/2}}

NOTE

I recommend you read how Artes changes the variables here. This is a mathematical approach to solving a software problem.