What is the solution to the system of equations y = -2x2 + 2 and y = 3?

Question

find solution of the system of equations What is the solution to the system of equations y = -2x² + 2 and y = 3?

1. 
   

Answer 1

You could graph the two equations

y=3 is a flat horizontal line

y=-2x^2+2 is a downward opening parabola with y intercept at y=2 or the point (0,2) which is also the vertex and maximum point.

The solution is where the two lines intersect, but they don't intersect as y=3 is above the maximum point of the parabola. There is no real solution. But there are imaginary solutions. They come in conjugate pairs.

y=y

-2x^2 + 2 = 3

x = + or - (1/-4)sqr(0^2 - 4)(-2)(-1) = + or - (1/4)sqr-8 = + or - (i/2)sqr2

2x^2 -2 = -3

2x^2 = -1

x^2 = -1/2

x = + square root of -1/2 = + or - isqr(1/2)

x = + (i/2)sqr2

check the solution

y=3 = -2x^2 +2 = -2[(i/2)sqr2] + 2

1 = -2[(i/2)sqr2]^2 = (2/4)2 = 1