Question

If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this.
6x − 2y = 2,
9x − 3y = 1

Answer 1

There is no solution, since the two equations correspond to parallel lines that do not intersect. In other words, they are incompatible equations.

The second equation can be rewritten
6x - 2y = 2/3, which clearly disagrees with
6x - 2y = 2.

I don't know what you mean by "set builder notation".