\(\displaystyle{y}={x}^{{{2}}}+{6}{x}+{9}\) (1)

\(x+y=3\)

Substitute eq 2 ... eq 1.

\(\displaystyle{3}-{x}={x}^{{{2}}}+{6}{x}+{9}\)

On simplification \(\displaystyle\rightarrow{3}-{x}-{x}^{{{2}}}-{6}{x}-{9}={0}\)

\(\displaystyle{x}^{{{2}}}+{7}{x}+{6}={0}\)

Factor \(\displaystyle\rightarrow\) \((x+1)(x+6)=0\)

Applying zero factor properly \(x+1=0\) or \(x+6=0\)

\(x=-1\) or \(x=-6\)

putting value of x in eq 2.

\(y=3-(-1), y=4\) or \(y=3-(-6), y=9\)

Solution set \(=\{(-1,4)(-6,9)\}\)