Two equations to be solved together, like:
y = ax²+bx+c = 0 and
y = mx + c
are called simultaneous equations.

To solve them you can plot them both on a graph and find where they cross each other.

The above display shows that a quadratic curve and a straight line can cross each other in 1 or 2 places, and may not cross at all. This tells you that the simultaneous equations y = ax²+bx+c and y = mx+c can have either 0, 1 or 2 answers.