This question already has an answer here:
If by eleminating $x$ between the equation $x² + ax + b = 0$ & $xy + l (x + y) + m = 0$, a quadratic in $y$ is formed whose roots are the same as those of the original quadratic in $x$. Then prove either $a = 2l$ & $b = m$ or $b + m = al$.
Today while we were solving this sum in class our professor told us that rather than directly eliminating $x$ from both the equations there is a shortcut method too.Since the equation after eliminating $x$ in $y$ is same as the the original quadratic in $x$ we can simply replace $y$ by $x$ in the second equation to form another quadratic. Then we can apply the condition for one root common or both roots common between this new quadratic and the original quadratic to reach final result.
But I didn't get why we can replace $y$ by $x$ in the second equation.Can someone please explain in detail?Thanks.