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Solve the system of equations.\newliney=x2−22x+9y = x^2 - 22x + 9\newliney=−x−29y = -x - 29\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=x2−22x+9y = x^2 - 22x + 9\newliney=−x−29y = -x - 29\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Set Equations Equal: Set the two equations equal to each other since they both equal yy.y=x2−22x+9y = x^2 - 22x + 9y=−x−29y = -x - 29So, x2−22x+9=−x−29x^2 - 22x + 9 = -x - 29
  2. Move and Simplify: Move all terms to one side to set the equation to zero and simplify.\newlinex2−22x+x+9+29=0x^2 - 22x + x + 9 + 29 = 0\newlinex2−21x+38=0x^2 - 21x + 38 = 0
  3. Factor Quadratic Equation: Factor the quadratic equation.\newline(x−19)(x−2)=0(x - 19)(x - 2) = 0
  4. Solve for x: Solve for x by setting each factor equal to zero.\newlinex−19=0x - 19 = 0 or x−2=0x - 2 = 0\newlineSo, x=19x = 19 or x=2x = 2
  5. Substitute x=19x = 19: Substitute x=19x = 19 into one of the original equations to find the corresponding yy value.\newlineUsing y=−x−29y = -x - 29:\newliney=−(19)−29y = -(19) - 29\newliney=−19−29y = -19 - 29\newliney=−48y = -48
  6. Substitute x=2x = 2: Substitute x=2x = 2 into one of the original equations to find the corresponding yy value.\newlineUsing y=−x−29y = -x - 29:\newliney=−(2)−29y = -(2) - 29\newliney=−2−29y = -2 - 29\newliney=−31y = -31

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