Bi-variate Non-Homogeneous Polynomial Conceptual Question

[knowLittle]

Homework Statement

I have found the roots of my polynomial:
$(2x+3y)^{2}-1 =0$
Roots are x=3n+2 & y=-2n-1, where n belongs to all Z.
What does it mean that the solution has arbitrary large coordinates?

The Attempt at a Solution

I think I know the basic concept of root. It could be that in this case the surface (has defined solutions) intersect some other plane at 0 in both points
Also, if it has arbitrary large coordinates as roots, it is because the axis of the surface or part of the surface runs through all solutions in the form above.
Am I right?

Thank you.

 

[Nino MMP]

Yes, you are correct. The fact that the coordinates of the roots have arbitrary large values means that as n increases, the values of x and y increase without bound. This in turn means that the solutions to the equation can be found in all parts of the coordinate plane, and not just in a finite area.