1. [5] Find the sum of all solutions for $x$ :
$$
\begin{aligned}
x y & =1 \\
x+y & =3
\end{aligned}
$$
Answer: 3 Substitute $3-x$ in for $y$ into the first equation:
$$
x(3-x)=1 \Leftrightarrow x^{2}-3 x+1=0
$$

This equation has two distinct roots, each of which corresponds to a possible solution $x$. The sum of the roots of the quadratic equation $a x^{2}+b x+c=0$ is $\frac{-b}{a}$, which in this case is 3 .