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Solve the system of equations.\newliney=−4xy = -4x\newlinex2+y2=612x^2 + y^2 = 612\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newliney=−4xy = -4x\newlinex2+y2=612x^2 + y^2 = 612\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute yy into second equation: Substitute yy from the first equation into the second equation.\newliney=−4xy = -4x\newlinex2+y2=612x^2 + y^2 = 612\newlinex2+(−4x)2=612x^2 + (-4x)^2 = 612
  2. Simplify the equation: Simplify the equation. x2+16x2=612x^2 + 16x^2 = 612 17x2=61217x^2 = 612
  3. Divide by 1717 for x2x^2: Divide both sides by 1717 to solve for x2x^2.x2=61217x^2 = \frac{612}{17}x2=36x^2 = 36
  4. Take square root for x: Take the square root of both sides to find x.\newlinex=±36x = \pm\sqrt{36}\newlinex=±6x = \pm6
  5. Substitute xx back for yy: Substitute xx back into the first equation to find yy.\newlineFor x=6x = 6: y=−4(6)=−24y = -4(6) = -24\newlineFor x=−6x = -6: y=−4(−6)=24y = -4(-6) = 24
  6. Write coordinates in exact form: Write the coordinates in exact form.\newlineFirst Coordinate: (6,−24)(6, -24)\newlineSecond Coordinate: (−6,24)(-6, 24)

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