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Solve the system of equations.\newlinex2+y2=180x^2 + y^2 = 180\newliney=−2xy = -2x\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newlinex2+y2=180x^2 + y^2 = 180\newliney=−2xy = -2x\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute and Simplify: Substitute y=−2xy = -2x into x2+y2=180x^2 + y^2 = 180.
    x2+(−2x)2=180x^2 + (-2x)^2 = 180
    x2+4x2=180x^2 + 4x^2 = 180
    5x2=1805x^2 = 180
  2. Divide and Solve: Divide both sides by 55 to solve for x2x^2.\newlinex^2 = rac{180}{5}\newlinex2=36x^2 = 36
  3. Take Square Root: Take the square root of both sides to find xx.\newlinex=±36x = \pm\sqrt{36}\newlinex=±6x = \pm6
  4. Find y Values: Substitute xx back into y=−2xy = -2x to find yy.
    For x=6x = 6: y=−2(6)=−12y = -2(6) = -12
    For x=−6x = -6: y=−2(−6)=12y = -2(-6) = 12
  5. Write Coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (6,−12)(6, -12)\newlineSecond Coordinate: (−6,12)(-6, 12)

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