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Solve the system of equations.\newliney=−14x−33y = -14x - 33\newliney=x2−26x+3y = x^2 - 26x + 3\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)

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Q. Solve the system of equations.\newliney=−14x−33y = -14x - 33\newliney=x2−26x+3y = x^2 - 26x + 3\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)
  1. Set Equations Equal: Set the two equations equal to each other since they both equal yy.−14x−33=x2−26x+3-14x - 33 = x^2 - 26x + 3
  2. Move Terms, Set to Zero: Move all terms to one side to set the equation to zero.\newlinex2−26x+14x+3+33=0x^2 - 26x + 14x + 3 + 33 = 0\newlinex2−12x+36=0x^2 - 12x + 36 = 0
  3. Factor Quadratic Equation: Factor the quadratic equation. (x−6)(x−6)=0(x - 6)(x - 6) = 0
  4. Solve for x: Solve for x by setting each factor equal to zero.\newlinex−6=0x - 6 = 0\newlinex=6x = 6
  5. Substitute xx for yy: Substitute xx back into one of the original equations to find yy. Using y=−14x−33y = -14x - 33, substitute x=6x = 6. y=−14(6)−33y = -14(6) - 33 y=−84−33y = -84 - 33 y=−117y = -117
  6. Write Coordinates: Write the coordinates in exact form.\newlineThe solution to the system is (6,−117)(6, -117).

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