No graph, no problem.

Question

How many solutions does this system of equations have?

3y-6x=12

5y+10=15x

Answer 1

If I divide the top by 3 and the bottom by 5...

y = 2x + 6

y = 3x - 2

I have two separate functions with different slopes, so I have ONE solution.

If they had the same slope, I'd have none, since they'd be parallel. If they were the same function, I'd have infinite solutions because they'd be the same line.