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Solve the system of equations.\newliney=−18x+47y = -18x + 47\newliney=x2−18x−34y = x^2 - 18x - 34\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newliney=−18x+47y = -18x + 47\newliney=x2−18x−34y = x^2 - 18x - 34\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute yy Equation: Substitute yy from the first equation into the second equation. This gives us −18x+47=x2−18x−34-18x + 47 = x^2 - 18x - 34.
  2. Simplify Equation: Simplify the equation by moving all terms to one side to set the equation to zero: 0=x2−34−470 = x^2 - 34 - 47.
  3. Combine Like Terms: Combine like terms to get the quadratic equation: 0=x2−810 = x^2 - 81.
  4. Factor Quadratic Equation: Factor the quadratic equation: 0=(x−9)(x+9)0 = (x - 9)(x + 9).
  5. Solve for x: Solve for x by setting each factor equal to zero: x−9=0x - 9 = 0 and x+9=0x + 9 = 0.
  6. Find Solutions for x: Find the two solutions for xx: x=9x = 9 and x=−9x = -9.
  7. Substitute x=9x = 9: Substitute x=9x = 9 into the first equation to find the corresponding yy value: y=−18(9)+47y = -18(9) + 47.
  8. Calculate yy for x=9x = 9: Calculate the yy value for x=9x = 9: y=−162+47y = -162 + 47.
  9. Substitute x=−9x = -9: Simplify to find the yy value: y=−115y = -115.
  10. Calculate yy for x=−9x = -9: Substitute x=−9x = -9 into the first equation to find the corresponding yy value: y=−18(−9)+47y = -18(-9) + 47.
  11. Write Coordinate Points: Calculate the yy value for x=−9x = -9: y=162+47y = 162 + 47.
  12. Write Coordinate Points: Calculate the yy value for x=−9x = -9: y=162+47y = 162 + 47.Simplify to find the yy value: y=209y = 209.
  13. Write Coordinate Points: Calculate the yy value for x=−9x = -9: y=162+47y = 162 + 47. Simplify to find the yy value: y=209y = 209. Write the solutions as coordinate points: The coordinate points are (9,−115)(9, -115) and (−9,209)(-9, 209).

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