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Solve the system of equations.\newliney=−5xy = -5x\newlinex2+y2=416x^2 + y^2 = 416\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=−5xy = -5x\newlinex2+y2=416x^2 + y^2 = 416\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=−5xy = -5x\newlinex2+y2=416x^2 + y^2 = 416\newlinex2+(−5x)2=416x^2 + (-5x)^2 = 416
  2. Simplify the equation: Simplify the equation. x2+25x2=416x^2 + 25x^2 = 416 26x2=41626x^2 = 416
  3. Divide by 2626: Divide both sides by 2626 to solve for x2x^2.\newlinex2=41626x^2 = \frac{416}{26}\newlinex2=16x^2 = 16
  4. Take square root: Take the square root of both sides to find xx.\newlinex=±16x = \pm\sqrt{16}\newlinex=±4x = \pm4
  5. Substitute xx back: Substitute xx back into the first equation to find yy.\newlineFor x=4x = 4: y=−5(4)=−20y = -5(4) = -20\newlineFor x=−4x = -4: y=−5(−4)=20y = -5(-4) = 20
  6. Write coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (4,−20)(4, -20)\newlineSecond Coordinate: (−4,20)(-4, 20)

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