I know, it is very simple, but I'm get stuck. Let I have two equations of straight lines on a plate.
For example: $2x + 3y + 5 = 0$; 3$x + 4y + 7 = 0$
What is the geometric meaning of a new line, that has been got by equaling of equations.
$2x + 3y + 5 = 3x + 4y + 7$;
$x + y + 2 = 0$
It is a line, lies exactly between them, isn't it?
I have a spirit of an old lecture repeats in my mind. "To find an intersection point of two functions you need to equal the equations..."
But if I let x = any constant and $y = - 2 - x$ , then I'll get a complete rubbish.
What do I forget?