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Solve the system of equations.\newliney=38x+41y = 38x + 41\newliney=x2+38x−40y = x^2 + 38x - 40\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=38x+41y = 38x + 41\newliney=x2+38x−40y = x^2 + 38x - 40\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute yy in second equation: Substitute yy from the first equation into the second equation since they are both equal to yy. This gives us the equation 38x+41=x2+38x−4038x + 41 = x^2 + 38x - 40.
  2. Simplify the equation: Simplify the equation by subtracting 38x38x from both sides and subtracting 4141 from both sides to get 0=x2−40−410 = x^2 - 40 - 41.
  3. Further simplify to x2−81x^2 - 81: Further simplify the equation to get 0=x2−810 = x^2 - 81.
  4. Factor the quadratic equation: Factor the quadratic equation to find the values of xx. This gives us (x−9)(x+9)=0(x - 9)(x + 9) = 0.
  5. Solve for xx: Set each factor equal to zero and solve for xx. This gives us x=9x = 9 and x=−9x = -9.
  6. Substitute x=9x = 9: Substitute x=9x = 9 into the first equation y=38x+41y = 38x + 41 to find the corresponding value of yy. This gives us y=38(9)+41y = 38(9) + 41.
  7. Calculate yy when x=9x = 9: Calculate the value of yy when x=9x = 9. This gives us y=342+41y = 342 + 41, which simplifies to y=383y = 383.
  8. Substitute x=−9x = -9: Substitute x=−9x = -9 into the first equation y=38x+41y = 38x + 41 to find the corresponding value of yy. This gives us y=38(−9)+41y = 38(-9) + 41.
  9. Calculate yy when x=−9x = -9: Calculate the value of yy when x=−9x = -9. This gives us y=−342+41y = -342 + 41, which simplifies to y=−301y = -301.

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