1. Determine the set $A=\left\{(x, y) \in \mathbb{Z} \times \mathbb{Z} \mid x+y=1, x^{2}+2 x+y^{2}=9\right\}$.
1. Substituting $y=1-x$ into the equation $x^{2}+2 x+y^{2}=9$, we get $x^{2}=4$, from which $x= \pm 2$. We deduce that $A=\{(2,-1),(-2,3)\}$.