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Solve the system of equations.\newliney=x2+14x+40y = x^2 + 14x + 40\newliney=38x−104y = 38x - 104\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)

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Solve a nonlinear system of equationsright chevron icon

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Q. Solve the system of equations.\newliney=x2+14x+40y = x^2 + 14x + 40\newliney=38x−104y = 38x - 104\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)
  1. Substitute yy into second equation: Substitute yy from the first equation into the second equation: x2+14x+40=38x−104x^2 + 14x + 40 = 38x - 104.
  2. Rearrange equation to set to 00: Rearrange the equation to set it to 00: x2+14x+40−38x+104=0x^2 + 14x + 40 - 38x + 104 = 0.
  3. Simplify the equation: Simplify the equation: x2−24x+144=0x^2 - 24x + 144 = 0.
  4. Factor the quadratic equation: Factor the quadratic equation: (x−12)2=0(x - 12)^2 = 0.
  5. Solve for x: Solve for x: x=12x = 12.
  6. Substitute xx back to find yy: Substitute xx back into the first equation to find yy: y=122+14×12+40y = 12^2 + 14 \times 12 + 40.
  7. Calculate y: Calculate y: y=144+168+40y = 144 + 168 + 40.
  8. Add numbers to find y: Add the numbers to find y: y=352y = 352.

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