System of linear equations

Question

Suppose that you were entering a system of linear equations and f(x)=x^2+3x-2 and g(x)=3x^2+2x+1, what would the set pair for both equations be?

Answer 1

x^2 +3x -2 = 3x^2 +2x +1

2x^2 -x +3 = 0

x = 1/4 + or - (1/4)sqr(1-24) = 1/4 + or - (1/4)isqr23 = (1+isqr23)/4 or (1-isqr23)/4

y = 0

(x,y) = ((1+isqr23)/4, 0) or ((1-isqr23)/4, 0)

the two parabolas never intersect, algebraically there's no real solution, just imaginary solutions

the functions are quadratic parabolas, not linear lines.

the parabola on top is narrower, the one on the bottom is wider, so there are no points of intersection of the graphs.