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)