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Solve the system of equations.\newliney=x2+30x+12y = x^2 + 30x + 12\newliney=42x−24y = 42x - 24\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)

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Q. Solve the system of equations.\newliney=x2+30x+12y = x^2 + 30x + 12\newliney=42x−24y = 42x - 24\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)
  1. Set Equations Equal: Set the two equations equal to each other since they both equal yy.x2+30x+12=42x−24x^2 + 30x + 12 = 42x - 24
  2. Subtract and Add: Subtract 42x42x and add 2424 to both sides to get the quadratic equation.\newlinex2−12x+36=0x^2 - 12x + 36 = 0
  3. Factor Quadratic Equation: Factor the quadratic equation. (x−6)2=0(x - 6)^2 = 0
  4. Solve for x: Solve for x by taking the square root of both sides.\newlinex−6=0x - 6 = 0\newlinex=6x = 6
  5. Substitute xx: Substitute x=6x = 6 back into one of the original equations to find yy.\newliney=42(6)−24y = 42(6) - 24\newliney=252−24y = 252 - 24\newliney=228y = 228
  6. Write Coordinates: Write the coordinates in exact form.\newlineThe solution to the system is (6,228)(6, 228).

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