Question

Solve the nonlinear system of equations

Answer 1

Answer:

  There are no real solutions. The complex solutions are ...

  (x, y) = (2.5-i√1.75, -2.5+i√1.75)  or  (2.5+i1.75, -2.5-i1.75)

Step-by-step explanation:

Subtract the first equation from the second.

  y -y = (x^2 -6x +8) -(-x)

  0 = x^2 -5x +8

Rewrite to facilitate completing the square:

  x^2 -5x = -8

  x^2 -5x +6.25 = -1.75 . . . . . add 6.25 to complete the square

  (x -2.5)^2 = -1.75 . . . . . write as a square

  x -2.5 = ±i√1.75 . . . . . . take the square root

  x = 2.5 ± i√1.75 . . . . . . add 2.5; y is the opposite of this

Solutions are ...

• x = 2.5 +i√1.75, y = -2.5 -i√1.75
• x = 2.5 -i√1.75, y = -2.5 +i√1.75

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The graph shows the equations have no point of intersection, meaning there are no real solutions. The complex solutions are shown above.