3. If real numbers $a, b, x$ and $y$ satisfy the system of equations
$$
\left\{\begin{array}{l}
a x+b y=3, \\
a x^{2}+b y^{2}=7, \\
a x^{3}+b y^{3}=6, \\
a x^{4}+b y^{4}=42 .
\end{array}\right.
$$

Find the value of $a x^{5}+b y^{5}$.
(8th American Invitational Mathematics Examination)
3. Let $T_{n}=a x^{n}+b y^{n}$, where $x, y$ are the two real roots of the quadratic equation $t^{2}=p t+q$. According to Newton's formula, we have $T_{5}=p T_{4}+q T_{3}=-14 \times 42+38 \times 16=20$, i.e., $a x^{5}+b y^{5}=20$.