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Solve the system of equations.\newliney=37x2−31x−13y = 37x^2 - 31x - 13\newliney=−31x+24y = -31x + 24\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newliney=37x2−31x−13y = 37x^2 - 31x - 13\newliney=−31x+24y = -31x + 24\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Set Equations Equal: Set the two equations equal to each other to find the xx-values where they intersect.37x2−31x−13=−31x+2437x^2 - 31x - 13 = -31x + 24
  2. Form Quadratic Equation: Move all terms to one side to form a quadratic equation. \newline37x2−31x−13+31x−24=037x^2 - 31x - 13 + 31x - 24 = 0\newline37x2−37=037x^2 - 37 = 0
  3. Simplify and Factor: Simplify the equation by combining like terms.\newline37x2−37=037x^2 - 37 = 0\newline37(x2−1)=037(x^2 - 1) = 0
  4. Solve for xx: Factor the quadratic equation.37(x−1)(x+1)=037(x - 1)(x + 1) = 0
  5. Find y-Values: Solve for xx by setting each factor equal to zero.\newline(x−1)=0(x - 1) = 0 or (x+1)=0(x + 1) = 0\newlinex=1x = 1 or x=−1x = -1
  6. Write Coordinates: Find the corresponding yy-values by substituting the xx-values into one of the original equations. Let's use y=−31x+24y = -31x + 24.
    For x=1x = 1: y=−31(1)+24=−31+24=−7y = -31(1) + 24 = -31 + 24 = -7
    For x=−1x = -1: y=−31(−1)+24=31+24=55y = -31(-1) + 24 = 31 + 24 = 55
  7. Write Coordinates: Find the corresponding yy-values by substituting the xx-values into one of the original equations. Let's use y=−31x+24y = -31x + 24.\newlineFor x=1x = 1: y=−31(1)+24=−31+24=−7y = -31(1) + 24 = -31 + 24 = -7\newlineFor x=−1x = -1: y=−31(−1)+24=31+24=55y = -31(-1) + 24 = 31 + 24 = 55Write the coordinates in exact form.\newlineFirst Coordinate: (1,−7)(1, -7)\newlineSecond Coordinate: (−1,55)(-1, 55)

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