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Solve the system of equations.\newliney=x2+18x+36y = x^2 + 18x + 36\newliney=4x+12y = 4x + 12\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newliney=x2+18x+36y = x^2 + 18x + 36\newliney=4x+12y = 4x + 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+18x+36y = x^2 + 18x + 36y=4x+12y = 4x + 12So, x2+18x+36=4x+12x^2 + 18x + 36 = 4x + 12.
  2. Subtract and Simplify: Subtract 4x+124x + 12 from both sides to set the equation to zero.\newlinex2+18x+36−4x−12=0x^2 + 18x + 36 - 4x - 12 = 0\newlineThis simplifies to x2+14x+24=0x^2 + 14x + 24 = 0.
  3. Factor Quadratic Equation: Factor the quadratic equation. \newline(x+2)(x+12)=0(x + 2)(x + 12) = 0
  4. Solve for x: Solve for x by setting each factor equal to zero.\newlinex+2=0x + 2 = 0 or x+12=0x + 12 = 0\newlineThis gives us x=−2x = -2 or x=−12x = -12.
  5. Substitute x=−2x = -2: Substitute x=−2x = -2 into one of the original equations to find the corresponding yy value.\newlineUsing y=4x+12y = 4x + 12:\newliney=4(−2)+12y = 4(-2) + 12\newliney=−8+12y = -8 + 12\newliney=4y = 4\newlineSo one intersection point is (−2,4)(-2, 4).
  6. Substitute x=−12x = -12: Substitute x=−12x = -12 into one of the original equations to find the corresponding yy value.\newlineUsing y=4x+12y = 4x + 12:\newliney=4(−12)+12y = 4(-12) + 12\newliney=−48+12y = -48 + 12\newliney=−36y = -36\newlineSo the other intersection point is (−12,−36)(-12, -36).

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