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Solve the system of equations.\newliney=−20x−22y = -20x - 22\newliney=x2−37x+20y = x^2 - 37x + 20\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Solve a system of linear and quadratic equations: parabolasright chevron icon

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Q. Solve the system of equations.\newliney=−20x−22y = -20x - 22\newliney=x2−37x+20y = x^2 - 37x + 20\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 since they both equal yy.−20x−22=x2−37x+20-20x - 22 = x^2 - 37x + 20
  2. Move Terms to One Side: Move all terms to one side to set the equation to zero.\newlinex2−37x+20+20x+22=0x^2 - 37x + 20 + 20x + 22 = 0\newlinex2−17x+42=0x^2 - 17x + 42 = 0
  3. Factor Quadratic Equation: Factor the quadratic equation. \newline(x−14)(x−3)=0(x - 14)(x - 3) = 0
  4. Solve for x: Solve for x by setting each factor equal to zero.\newlinex−14=0x - 14 = 0 or x−3=0x - 3 = 0\newlinex=14x = 14 or x=3x = 3
  5. Substitute x Values: Substitute x=14x = 14 into one of the original equations to find yy.\newliney=−20(14)−22y = -20(14) - 22\newliney=−280−22y = -280 - 22\newline$y = \(-302\)
  6. Find y Values: Substitute \(x = 3\) into one of the original equations to find \(y\).\(y = -20(3) - 22\)\(y = -60 - 22\)\(y = -82\)
  7. Write Coordinates: Write the coordinates in exact form.\(\newline\)First Coordinate: \((14, -302)\)\(\newline\)Second Coordinate: \((3, -82)\)

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