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Solve the system of equations.\newliney=29x−50y = 29x - 50\newliney=x2+43x−37y = x^2 + 43x - 37\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=29x−50y = 29x - 50\newliney=x2+43x−37y = x^2 + 43x - 37\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: x2+43x−37=29x−50x^2 + 43x - 37 = 29x - 50.
  2. Rearrange to set to zero: Rearrange the equation to set it to zero: x2+43x−29x−37+50=0x^2 + 43x - 29x - 37 + 50 = 0.
  3. Simplify the equation: Simplify the equation: x2+14x+13=0x^2 + 14x + 13 = 0.
  4. Factor the quadratic equation: Factor the quadratic equation: (x+1)(x+13)=0(x + 1)(x + 13) = 0.
  5. Solve for x: Solve for x: x=−1x = -1 or x=−13x = -13.
  6. Substitute x=−1x = -1: Substitute x=−1x = -1 into the first equation to find yy: y=29(−1)−50y = 29(-1) - 50.
  7. Calculate yy when x=−1x = -1: Calculate yy when x=−1x = -1: y=−29−50y = -29 - 50.
  8. Simplify to find y: Simplify to find y: y=−79y = -79.
  9. Substitute x=−13x = -13: Substitute x=−13x = -13 into the first equation to find yy: y=29(−13)−50y = 29(-13) - 50.
  10. Calculate yy when x=−13x = -13: Calculate yy when x=−13x = -13: y=−377−50y = -377 - 50.
  11. Simplify to find y: Simplify to find y: y=−427y = -427.

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