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Solve the system of equations.\newlinex=−3yx = -3y\newlinex2+y2=360x^2 + y^2 = 360\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newlinex=−3yx = -3y\newlinex2+y2=360x^2 + y^2 = 360\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute and Simplify: Substitute x=−3yx = -3y into the second equation x2+y2=360x^2 + y^2 = 360.
    (−3y)2+y2=360(-3y)^2 + y^2 = 360
    9y2+y2=3609y^2 + y^2 = 360
  2. Combine Like Terms: Combine like terms. 10y2=36010y^2 = 360
  3. Divide and Solve: Divide both sides by 1010 to solve for y2y^2.\newliney2=36y^2 = 36
  4. Find yy: Take the square root of both sides to find yy.\newliney=±6y = \pm 6
  5. Substitute and Find xx: Substitute yy back into x=−3yx = -3y to find xx.\newlineFor y=6y = 6: x=−3(6)=−18x = -3(6) = -18\newlineFor y=−6y = -6: x=−3(−6)=18x = -3(-6) = 18
  6. Write Coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (−18,6)(-18, 6)\newlineSecond Coordinate: (18,−6)(18, -6)

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