The more bizarre thing to say is “try to imagine that each simultaneous equation is a road of sorts in the space where the simultaneous equations exist, and the solution to the simultaneous equations is the intersection of the simultaneous equations.”
Let’s hit it with a simpler example.
Assume we have the “requirement” that x=4 be true. This requirement creates a line in 2D space.
Next assume we have the insistence that y=3 be true. This insistence creates a line in 2D space.
The “answer” where the requirement and the insistence are both true is the point (4,3).
If you like this and you want a challenge, change the story so that that we are in a 3D space instead of a 2D space. Be prepared to create planes and ask yourself if the intersection of two planes is a line.