Question

Systems of equations with different slopes and different y-intercepts have one solution.

Always

Sometimes

Never

Answer 1

never

Answer 2

if these are lines in the x-y plane, then different slopes means the lines are not parallel. Not parallel means they meet. where they meet is the solution to the system if there are only 2 lines.

If there are only 2 equations, there would always be a solution.
If there are more than 2 equations (lines), then there may be a solution (where all 3 lines meet at the same spot), or there may not be a solution

I would say the answer is sometimes.