<s>[INST] How to solve system of two equation with two unknown and using substitution? $$\begin{align}
a^2 - b^2 = 3\\
a \cdot b = 2
\end{align}$$
In aforementioned equations, we can mentally find out the value of $a = 2, b = 1$. But what is the general way to solve this system algebraically? 
I tried to use substitution but I got stuck. Rearranging two equations to $a^2=b^2+3$ and $a^2 \cdot b^2 = 2^2$ we will get:
$$ (b^2 + 3) \cdot b^2 = 4\\
\rightarrow b^4 + 3b^2 = 4\\
\rightarrow b^2(b^2 + 3) = 4\\
$$
Then what?
Alternatively can we solve by elimination?
 [/INST] Your last equation, $b^2+3b^2-4=0$ is a quadratic in $b^2$.  You can define $c=b^2$ and find $c^2+3c-4=0$.  Maybe you can factor this, if not you can use the quadratic formula.  Solve for $c$, then take the square root to get $b$.  This works for quartics that only have the even power terms.
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