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Solve the system of equations.\newlinex2+y2=640x^2 + y^2 = 640\newliney=−3xy = -3x\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=640x^2 + y^2 = 640\newliney=−3xy = -3x\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute y=−3xy = -3x: Substitute y=−3xy = -3x into x2+y2=640x^2 + y^2 = 640.
    x2+(−3x)2=640x^2 + (-3x)^2 = 640
    x2+9x2=640x^2 + 9x^2 = 640
    10x2=64010x^2 = 640
  2. Divide by 1010: Divide both sides by 1010 to solve for x2x^2.\newlinex2=64x^2 = 64
  3. Take square root: Take the square root of both sides to find xx.x=±8x = \pm 8
  4. Substitute xx back: Substitute xx back into y=−3xy = -3x to find yy.\newlineFor x=8x = 8: y=−3(8)=−24y = -3(8) = -24\newlineFor x=−8x = -8: y=−3(−8)=24y = -3(-8) = 24
  5. Write coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (8,−24)(8, -24)\newlineSecond Coordinate: (−8,24)(-8, 24)

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