How do you find the solutions to a system of equations involving quadratic functions and other functions?

Since no example is being given, let's take for instance 2 functions, one quadratic & the second linear:

y₁=ax²+bx+c & the second y₂=mx+b

The solution of those function is the coordinates (x,y) where both meet at a point . In this case (& in all other cases) you have to state that  y₁=y₂

ax²+bx+c = mx + b & solve

example

y₁= x²+3x-1 & y₂=x-2

x²+3x-1 = x-2==>x²+3x-1-x+2 = x²+2x+1

Find the root of  x²+2x+1 & you will find x'=x" -1
We have found the value of x= - 1, to find y, just plug into any of the equation x by its value & you will find y=-3
So the solution of this system of equation is at their pint(s) of intersection, that is (-1,-3)