Can anyone explain to me how to find a locus of any point

Matt and brian were solving a system of equations. they both noticed that the two lines had the same slope. brian said that because each line in the system had the same slope, the two lines had to be parallel, which meant the solution to the system was "no solution" matt disagreed, and said they should also look at the y-intercepts before determining how many solutions there were. who is correct?

How many real and imaginary solutions does the equation x^2-3x=-2x-7 have?

What could explain what happened when the time was equal to 120 minutes