Question 15
Determine all quadruples $(a, b, c, d)$ of real numbers satisfying the following system of equations.
$$
\begin{aligned}
ab + ac &= 3b + 3c \\
bc + bd &= 5c + 5d \\
ac + cd &= 7a + 7d \\
ad + bd &= 9a + 9b
\end{aligned}
$$
$$
\begin{aligned}
ab + ac &= 3b + 3c \\
bc + bd &= 5c + 5d \\
ac + cd &= 7a + 7d \\
ad + bd &= 9a + 9b
\end{aligned}
$$