<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] HINT:
$$\implies b^4+3b^2-4=0\iff (b^2+4)(b^2-1)=0$$
Then from the second equation, find corresponding value of $a$ for each value of $b$
Then, check whether each pair of $(a,b)$ satisfy the first

Alternatively, $$(a^2+b^2)^2=(a^2-b^2)^2+(2ab)^2$$
</s>