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Solve the system of equations.\newliney=3x2−36x−21y = 3x^2 - 36x - 21\newliney=−36x−18y = -36x - 18\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)\newline

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Q. Solve the system of equations.\newliney=3x2−36x−21y = 3x^2 - 36x - 21\newliney=−36x−18y = -36x - 18\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)\newline
  1. Set Equations Equal: Set the two equations equal to each other to find the xx-values where the graphs intersect.\newliney=3x2−36x−21y = 3x^2 - 36x - 21\newliney=−36x−18y = -36x - 18\newline3x2−36x−21=−36x−183x^2 - 36x - 21 = -36x - 18
  2. Simplify Equation: Simplify the equation by adding 36x36x and 2121 to both sides.\newline3x2−36x−21+36x+21=−36x−18+36x+213x^2 - 36x - 21 + 36x + 21 = -36x - 18 + 36x + 21\newline3x2=33x^2 = 3
  3. Isolate x2x^2: Divide both sides by 33 to isolate x2x^2.\newline3x23=33\frac{3x^2}{3} = \frac{3}{3}\newlinex2=1x^2 = 1
  4. Solve for x: Take the square root of both sides to solve for x.\newlinex2=1\sqrt{x^2} = \sqrt{1}\newlinex=1x = 1 or x=−1x = -1
  5. Find y-values: Substitute the x-values back into one of the original equations to find the corresponding y-values.\newlineFor x=1x = 1:\newliney=−36x−18y = -36x - 18\newliney=−36(1)−18y = -36(1) - 18\newliney=−36−18y = -36 - 18\newliney=−54y = -54
  6. Substitute x-values: Substitute the second x-value into the same equation.\newlineFor x=−1x = -1:\newliney=−36x−18y = -36x - 18\newliney=−36(−1)−18y = -36(-1) - 18\newliney=36−18y = 36 - 18\newliney=18y = 18
  7. Write Coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (1,−54)(1, -54)\newlineSecond Coordinate: (−1,18)(-1, 18)

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