To determine if \((0, 0)\) is a solution to the inequality \(y \leq x + 7\), we can substitute \(x = 0\) and \(y = 0\) into the inequality:
\[ 0 \leq 0 + 7 \]
This simplifies to:
\[ 0 \leq 7 \]
This statement is true. Therefore, \((0, 0)\) is indeed a solution to the inequality \(y \leq x + 7\).