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Solve the system of equations.\newliney=−26x+48y = -26x + 48\newliney=x2−26x−33y = x^2 - 26x - 33\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newliney=−26x+48y = -26x + 48\newliney=x2−26x−33y = x^2 - 26x - 33\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute y Equation: Substitute yy from the first equation into the second equation: y=x2−26x−33y = x^2 - 26x - 33 becomes −26x+48=x2−26x−33-26x + 48 = x^2 - 26x - 33.
  2. Simplify Equation: Simplify the equation by adding 26x26x to both sides and subtracting 4848 from both sides: 0=x2−810 = x^2 - 81.
  3. Factor Quadratic Equation: Factor the quadratic equation: 0=(x−9)(x+9)0 = (x - 9)(x + 9).
  4. Solve for x: Solve for x by setting each factor equal to zero: x−9=0x - 9 = 0 or x+9=0x + 9 = 0.
  5. Find x-values: Find the two x-values: x=9x = 9 or x=−9x = -9.
  6. Substitute x=9x=9: Substitute x=9x = 9 into the first equation to find the corresponding y-value: y=−26(9)+48y = -26(9) + 48.
  7. Calculate yy for x=9x=9: Calculate the yy-value for x=9x = 9: y=−234+48y = -234 + 48.
  8. Simplify yy for x=9x=9: Simplify to find the yy-value: y=−186y = -186.
  9. Substitute x=−9x=-9: Substitute x=−9x = -9 into the first equation to find the corresponding y-value: y=−26(−9)+48y = -26(-9) + 48.
  10. Calculate yy for x=−9x=-9: Calculate the yy-value for x=−9x = -9: y=234+48y = 234 + 48.
  11. Simplify yy for x=−9x=-9: Simplify to find the yy-value: y=282y = 282.
  12. Write Coordinate Points: Write the solution as coordinate points: (9,−186)(9, -186) and (−9,282)(-9, 282).

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