Another question on solving simultaneous equations

1

x+y+z=1 and x+y=1 and x+y-z=1 are 3 equations. Algebraically, I get that there are infinite solutions.

Graphically, on desmos 3D Visualisation - Equations - Solutions | Desmos
I get this. The lines x=k and y=1-k are on the plane z=0 So, I see that the solutions are many points moving in a line along the plane z= 0.

Would a line joining these points with different k not be a solution to the simultaneous equation? Instead of saying it is infinite, could we not say it is a line?

Or is it that I should treat each k separately, then I get a point for k=0, another point for (0, 1, 0)
k = 1 (1, 0, 0) etc and many other real numbers in between and these infinite points are the infinite distinct solutions?

2

As I just wrote for an earlier question, due to our limited resources we are able only to address Calculus-related questions. We do hope to build to be able to help with other topics in the future, and for now hope you’ll be able to get the answers to your great questions elsewhere. : )