<s>[INST] Why does Solving system of quadratic equations gives extra roots? Consider these system of Equations
\begin{align*}
\begin{cases}
x^2+4x+4=0\\\\
x^2+5x+6=0
\end{cases}
\end{align*}
For solving them
We have
Method 1-
Subtract both equations
So
$-x-2=0$
Hence,
$x=-2$
Method-2
Add both equations
$2x^2+9x+10=0$
After applying quadratic formula,we get
$x=-2$ or $x=-5/2$. But only $x=-2$ satisfies the system of equation.
Why is the $-5/2$ not satisying the system of equations,what is intuition behind the error in method 2?
 [/INST] HINT
You can factor both polynomials according to your preferred method in order to obtain:
\begin{align*}
\begin{cases}
x^{2} + 4x + 4 = 0\\\\
x^{2} + 5x + 6 = 0
\end{cases} \Longleftrightarrow
\begin{cases}
(x+2)^{2} = 0\\\\
(x+2)(x+3) = 0
\end{cases}
\end{align*}
Can you take it from here?
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