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Solve the system of equations.\newlinex2+y2=180x^2 + y^2 = 180\newlinex=2yx = 2y\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\newlinex=2yx = 2y\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute into equation: Substitute x=2yx = 2y into x2+y2=180x^2 + y^2 = 180.
    (2y)2+y2=180(2y)^2 + y^2 = 180
    4y2+y2=1804y^2 + y^2 = 180
    5y2=1805y^2 = 180
  2. Solve for y2y^2: Divide both sides by 55 to solve for y2y^2.\newliney2=1805y^2 = \frac{180}{5}\newliney2=36y^2 = 36
  3. Find yy: Take the square root of both sides to find yy.\newliney=±36y = \pm\sqrt{36}\newliney=±6y = \pm6
  4. Find xx values: Substitute yy values into x=2yx = 2y to find corresponding xx values.\newlineFor y=6y = 6: x=2(6)=12x = 2(6) = 12\newlineFor y=−6y = -6: x=2(−6)=−12x = 2(-6) = -12
  5. Write coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (12,6)(12, 6)\newlineSecond Coordinate: (−12,−6)(-12, -6)

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