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Solve the system of equations.\newliney=x2−2x−2y = x^2 - 2x - 2\newliney=−3x+18y = -3x + 18\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=x2−2x−2y = x^2 - 2x - 2\newliney=−3x+18y = -3x + 18\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.x2−2x−2=−3x+18x^2 - 2x - 2 = -3x + 18
  2. Move Terms, Set to Zero: Move all terms to one side to set the equation to zero.\newlinex2−2x+3x−2−18=0x^2 - 2x + 3x - 2 - 18 = 0\newlinex2+x−20=0x^2 + x - 20 = 0
  3. Factor Quadratic Equation: Factor the quadratic equation. \newline(x+5)(x−4)=0(x + 5)(x - 4) = 0
  4. Solve for x: Set each factor equal to zero and solve for x.\newlinex+5=0x + 5 = 0 or x−4=0x - 4 = 0\newlinex=−5x = -5 or x=4x = 4
  5. Substitute xx, Find yy: Substitute x=−5x = -5 into the second equation to find yy.y=−3(−5)+18y = -3(-5) + 18y=15+18y = 15 + 18y=33y = 33
  6. Write Coordinates: Substitute x=4x = 4 into the second equation to find yy.\newliney=−3(4)+18y = -3(4) + 18\newliney=−12+18y = -12 + 18\newline$y = \(6\)
  7. Write Coordinates: Substitute \(x = 4\) into the second equation to find \(y\).\(y = -3(4) + 18\)\(y = -12 + 18\)\(y = 6\)Write the coordinates in exact form.First Coordinate: \((-5, 33)\)Second Coordinate: \((4, 6)\)

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