\section*{Problem 4 - V01004}

Determine the unknowns from:

\[
2^{x} \cdot 2^{y}=2^{22} \quad(1) \quad ; \quad x-y=4
\]
}

We can rewrite (1) as

\[
2^{x} \cdot 2^{y}=2^{x+y}=2^{22}
\]

so we need to solve the linear system of equations

\[
x+y=22 \quad(3) \quad, \quad x-y=4
\]

From (4) it follows that \(x=y+4\) and substituting this result into (3), we get

\[
x+y=(y+4)+y=2 y+4=22
\]

and thus \(y=9\) and therefore \(x=13\).