[tex]\begin{cases}x+y=-7 \\y = x^2 + 4x -3 \end{cases}\\\\\begin{cases} y=-x-7 \\ -x-7 = x^2 + 4x -3 \end{cases}\\\\\begin{cases} y=-x-7 \\ x^2 + 4x -3+7+-x=0\end{cases} \\\\\begin{cases} y=-x-7- \\ x^2 + 4x +4=0\end{cases} \\\\ x^2 + 53x +4=0\\\\a=1,\ b=5,\ c=4\\\\\Delta =b^2-4ac=5^2-4*1*4=25-16=9[/tex]
[tex]\sqrt{\Delta }=\sqrt{9}=3\\\\x_{1}=\frac{-b-\sqrt{\Delta } }{2a}=\frac{-5-3}{2*1}=\frac{-8}{2}=-4\\\\x_{2}=\frac{-b+\sqrt{\Delta } }{2a}=\frac{-5+3}{2*1}=\frac{-2}{2}=-1\\\\\begin{cases}y=-x-7 \\x=-4\end{cases}\ \ \ \vee \ \ \ \begin{cases}y=-x-7 \\x=-1\end{cases}\\\\\begin{cases}y=4-7 \\x=-4\end{cases}\ \ \ \vee \ \ \ \begin{cases}y=1-7 \\x=-1\end{cases}\\\\\begin{cases}y=-3 \\x=-4\end{cases}\ \ \ \vee \ \ \ \begin{cases}y=-6 \\x=-1\end{cases}[/tex]
