Question

How many solutions are there to the following system of equations? y=(x^2)-(5x)+3 and y=x-6

Answer 1

I don't know if there is a faster way, but I would substitute x-6 into y=(x^2)-(5x)+3 to get
x-6=(x^2)-(5x)+3, then move everything to one side to set the equation equal to 0, then find the discriminant with \[\sqrt{b^2-4ac}\]

Answer 2

If the discriminant is 0, one solution. Negative, no solutions. Positive, 2 solutions.

Answer 3

it has one solution