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Solve the system of equations.\newliney=x2−31x−30y = x^2 - 31x - 30\newliney=−21x−46y = -21x - 46\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=x2−31x−30y = x^2 - 31x - 30\newliney=−21x−46y = -21x - 46\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.x2−31x−30=−21x−46x^2 - 31x - 30 = -21x - 46
  2. Form Quadratic Equation: Move all terms to one side to form a quadratic equation.\newlinex2−31x+21x−30+46=0x^2 - 31x + 21x - 30 + 46 = 0\newlinex2−10x+16=0x^2 - 10x + 16 = 0
  3. Factor Quadratic: Factor the quadratic equation.\newline(x−8)(x−2)=0(x - 8)(x - 2) = 0
  4. Solve for x: Solve for x by setting each factor equal to zero.\newlinex−8=0x - 8 = 0 or x−2=0x - 2 = 0\newlinex=8x = 8 or x=2x = 2
  5. Substitute xx for yy: Substitute x=8x = 8 into the second equation to find yy.\newliney=−21(8)−46y = -21(8) - 46\newliney=−168−46y = -168 - 46\newliney=−214y = -214
  6. Find Coordinates: Substitute x=2x = 2 into the second equation to find yy.y=−21(2)−46y = -21(2) - 46y=−42−46y = -42 - 46y=−88y = -88
  7. Find Coordinates: Substitute x=2x = 2 into the second equation to find yy.y=−21(2)−46y = -21(2) - 46y=−42−46y = -42 - 46y=−88y = -88Write the coordinates in exact form.\newlineFirst Coordinate: (8,−214)(8, -214)\newlineSecond Coordinate: (2,−88)(2, -88)

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