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Solve the system of equations.\newliney=−4xy = -4x\newlinex2+y2=68x^2 + y^2 = 68\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=68x^2 + y^2 = 68\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute yy: Substitute yy from the first equation into the second equation.\newliney=−4xy = -4x\newlinex2+y2=68x^2 + y^2 = 68\newlinex2+(−4x)2=68x^2 + (-4x)^2 = 68
  2. Simplify equation: Simplify the equation. x2+16x2=68x^2 + 16x^2 = 68 17x2=6817x^2 = 68
  3. Divide for x2x^2: Divide both sides by 1717 to solve for x2x^2.\newlinex2=6817x^2 = \frac{68}{17}\newlinex2=4x^2 = 4
  4. Take square root: Take the square root of both sides to find xx.x=±2x = \pm 2
  5. Substitute for y: Substitute xx back into the first equation to find yy. For x=2x = 2: y=−4(2)=−8y = -4(2) = -8 For x=−2x = -2: y=−4(−2)=8y = -4(-2) = 8
  6. Write coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (2,−8)(2, -8)\newlineSecond Coordinate: (−2,8)(-2, 8)

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