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Solve the system of equations.\newlinex2+y2=650x^2 + y^2 = 650\newliney=5xy = 5x\newline\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=650x^2 + y^2 = 650\newliney=5xy = 5x\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute y=5xy = 5x: Substitute y=5xy = 5x into x2+y2=650x^2 + y^2 = 650.\newlinex2+(5x)2=650x^2 + (5x)^2 = 650\newlinex2+25x2=650x^2 + 25x^2 = 650\newline26x2=65026x^2 = 650
  2. Divide by 2626: Divide both sides by 2626 to solve for x2x^2.\newlinex2=65026x^2 = \frac{650}{26}\newlinex2=25x^2 = 25
  3. Take square root: Take the square root of both sides to find xx.x=±5x = \pm 5
  4. Substitute xx back: Substitute xx back into y=5xy = 5x to find yy.\newlineFor x=5x = 5: y=5(5)=25y = 5(5) = 25\newlineFor x=−5x = -5: y=5(−5)=−25y = 5(-5) = -25
  5. Write coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (5,25)(5, 25)\newlineSecond Coordinate: (−5,−25)(-5, -25)

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