What this solving system of equations?
x+y=-3
y=x^2+4x+1

x = -4,  y = 1

x = -1,   y = -2

Step-by-step explanation:

(1)     x + y = -3                  (2)    y =

             y = -x - 3                   -x - 3 =  

                                                    (x + 4)(x + 1) = 0

                                                         x = -4  or x = -1

            y = -(-4) - 3 = 4 - 3 = 1

            y = -(-1) - 3 = 1 - 3 = -2

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: