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Solve the system of equations.\newliney=33x+11y = 33x + 11\newliney=x2+33x−25y = x^2 + 33x - 25\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newliney=33x+11y = 33x + 11\newliney=x2+33x−25y = x^2 + 33x - 25\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute yy: Substitute yy from the first equation into the second equation: y=x2+33x−25y = x^2 + 33x - 25 becomes 33x+11=x2+33x−2533x + 11 = x^2 + 33x - 25.
  2. Subtract and simplify: Subtract 33x33x from both sides to get 11=x2−2511 = x^2 - 25.
  3. Add and solve for x: Add 2525 to both sides to solve for xx: 11+25=x211 + 25 = x^2, which simplifies to 36=x236 = x^2.
  4. Take square root: Take the square root of both sides to find xx: x=±36x = \pm\sqrt{36}.
  5. Calculate xx values: Since 36\sqrt{36} is 66, we have x=±6x = \pm 6.
  6. Calculate yy for x=6x = 6: Plug x=6x = 6 into the first equation to find yy: y=33(6)+11y = 33(6) + 11.
  7. Calculate yy for x=−6x = -6: Calculate yy for x=6x = 6: y=198+11y = 198 + 11, which simplifies to y=209y = 209.
  8. Find solution points: Now plug x=−6x = -6 into the first equation to find yy: y=33(−6)+11y = 33(-6) + 11.
  9. Find solution points: Now plug x=−6x = -6 into the first equation to find yy: y=33(−6)+11y = 33(-6) + 11.Calculate yy for x=−6x = -6: y=−198+11y = -198 + 11, which simplifies to y=−187y = -187.
  10. Find solution points: Now plug x=−6x = -6 into the first equation to find yy: y=33(−6)+11y = 33(-6) + 11.Calculate yy for x=−6x = -6: y=−198+11y = -198 + 11, which simplifies to y=−187y = -187.The solution to the system of equations is the points where the two graphs intersect, which are (6,209)(6, 209) and (−6,−187)(-6, -187).

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