# How do we make a combined equation of a curve and a line?

How do we make a combined equation of a curve $$ax^2+2hxy+by^2+2gx+2fy+c=0$$ and line $$lx + my = n?$$

-

$$(ax^2+2hxy+by^2+2gx+2fy+c)\cdot(lx+my-n)=0$$
In assumption that $l^2+m^2\ne{0}$ is possible to solve the linear equation $lx+my=n$ with respect to one of variables, say $x: \;\;x=\dfrac{n-my}{l}$ and substitute it into the first equation