Math

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Hi,
I can't seem to figure out the answer to this problem.
Thanks to anyone who can help!

*Solve the system of equations. Write your solution(s) in the form (x,y).

y = x^2
x^2 + y^2 = 20

  • Math -

    x^2+x^4-20=0
    (x^2-4)(x^2+5)=0
    (x+2)(x-2)(x^2+5)=0

    x= +-2, x= +-sqrt(-5

    (2,4)(-2,4)(sqrt-5,-5)(-sqrt-5, -5)

  • Math -

    y + y^2 = 20

    y^2 + y - 20 = 0
    (y-4)(y+5) = 0
    y = 4 or y = -5
    y = 4 is easy, then x = -2 or +2
    y = -5 means x = i sqrt 5
    now go back and see which of those solutions work in the original
    if y = 4 and x = 2 then
    yes, y = x^2
    and
    yes, 4 + 16 = 20

    if y = 4 and x = -2 then
    yes, y = x^2
    yes, 4 + 16 = 20

    if y = -5 and x = i sqrt 5
    yes, y = x^2
    yes, -5 + 25 = 20

  • Math -

    I left out y = -5, x = -i sqrt 5
    y = (-isqrt5)^2 = -5 yes
    -5 + 25 = 20 yes

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