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Solve the system of equations.\newliney=x2−5x+30y = x^2 - 5x + 30\newliney=−24x−18y = -24x - 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=x2−5x+30y = x^2 - 5x + 30\newliney=−24x−18y = -24x - 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.x2−5x+30=−24x−18x^2 - 5x + 30 = -24x - 18
  2. Move Terms to One Side: Move all terms to one side to set the equation to zero.\newlinex2−5x+24x+30+18=0x^2 - 5x + 24x + 30 + 18 = 0\newlinex2+19x+48=0x^2 + 19x + 48 = 0
  3. Factor Quadratic Equation: Factor the quadratic equation. \newline(x+3)(x+16)=0(x + 3)(x + 16) = 0
  4. Solve for x: Set each factor equal to zero and solve for x.\newlinex+3=0x + 3 = 0 or x+16=0x + 16 = 0\newlinex=−3x = -3 or x=−16x = -16
  5. Substitute x Values: Substitute xx values into one of the original equations to find yy values.\newlineFor x=−3x = -3: y=−24(−3)−18y = -24(-3) - 18 which gives y=72−18y = 72 - 18 so y=54y = 54.\newlineFor x=−16x = -16: y=−24(−16)−18y = -24(-16) - 18 which gives y=384−18y = 384 - 18 so y=366y = 366.
  6. Write Coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (−3,54)(-3, 54)\newlineSecond Coordinate: (−16,366)(-16, 366)

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