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Solve the system of equations.\newliney=x2−24x−30y = x^2 - 24x - 30\newliney=−21x−12y = -21x - 12\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=x2−24x−30y = x^2 - 24x - 30\newliney=−21x−12y = -21x - 12\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.y=x2−24x−30y = x^2 - 24x - 30y=−21x−12y = -21x - 12x2−24x−30=−21x−12x^2 - 24x - 30 = -21x - 12
  2. Form Quadratic Equation: Move all terms to one side to form a quadratic equation.\newlinex2−24x−30+21x+12=0x^2 - 24x - 30 + 21x + 12 = 0\newlinex2−3x−18=0x^2 - 3x - 18 = 0
  3. Factor Quadratic: Factor the quadratic equation.\newline(x−6)(x+3)=0(x - 6)(x + 3) = 0
  4. Solve for x: Solve for x by setting each factor equal to zero.\newlinex−6=0x - 6 = 0 or x+3=0x + 3 = 0\newlinex=6x = 6 or x=−3x = -3
  5. Substitute and Find yy: Substitute xx values into the second equation to find corresponding yy values.\newlineFor x=6x = 6: y=−21(6)−12y = -21(6) - 12 which gives y=−126−12y = -126 - 12 so y=−138y = -138.\newlineFor x=−3x = -3: y=−21(−3)−12y = -21(-3) - 12 which gives y=63−12y = 63 - 12 so xx00.
  6. Write Coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (6,−138)(6, -138)\newlineSecond Coordinate: (−3,51)(-3, 51)

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