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Solve the system of equations.\newliney=24x−33y = 24x - 33\newliney=x2+50x−8y = x^2 + 50x - 8\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Solve a nonlinear system of equationsright chevron icon

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Q. Solve the system of equations.\newliney=24x−33y = 24x - 33\newliney=x2+50x−8y = x^2 + 50x - 8\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute yy into second equation: Substitute yy from the first equation into the second equation since they are both equal to yy. This gives us the equation 24x−33=x2+50x−824x - 33 = x^2 + 50x - 8.
  2. Rearrange and solve for x: Rearrange the equation to set it to zero and solve for x. This means we subtract 24x24x and add 3333 to both sides, resulting in x2+26x−25=0x^2 + 26x - 25 = 0.
  3. Factor quadratic equation: Factor the quadratic equation x2+26x−25x^2 + 26x - 25. The factors of −25-25 that add up to 2626 are 2525 and 11. So the factored form is (x+25)(x+1)=0(x + 25)(x + 1) = 0.
  4. Solve for x: Solve for x by setting each factor equal to zero. This gives us x+25=0x + 25 = 0 or x+1=0x + 1 = 0, which means x=−25x = -25 or x=−1x = -1.
  5. Substitute x=−25x = -25: Substitute x=−25x = -25 into the first equation y=24x−33y = 24x - 33 to find the corresponding yy value. This gives us y=24(−25)−33y = 24(-25) - 33, which simplifies to y=−600−33y = -600 - 33, resulting in y=−633y = -633.
  6. Substitute x=−1x = -1: Substitute x=−1x = -1 into the first equation y=24x−33y = 24x - 33 to find the corresponding yy value. This gives us y=24(−1)−33y = 24(-1) - 33, which simplifies to y=−24−33y = -24 - 33, resulting in y=−57y = -57.

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