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Solve the system of equations.\newliney=x2+10x−4y = x^2 + 10x - 4\newliney=2x+29y = 2x + 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+10x−4y = x^2 + 10x - 4\newliney=2x+29y = 2x + 29\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute yy into first equation: Substitute yy from the second equation into the first equation: x2+10x−4=2x+29x^2 + 10x - 4 = 2x + 29.
  2. Rearrange to set to 00: Rearrange the equation to set it to 00: x2+10x−4−2x−29=0x^2 + 10x - 4 - 2x - 29 = 0.
  3. Simplify the equation: Simplify the equation: x2+8x−33=0x^2 + 8x - 33 = 0.
  4. Factor the quadratic equation: Factor the quadratic equation: (x+11)(x−3)=0(x + 11)(x - 3) = 0.
  5. Solve for x: Solve for x: x=−11x = -11 or x=3x = 3.
  6. Substitute x=−11x = -11: Substitute x=−11x = -11 into y=2x+29y = 2x + 29 to find yy: y=2(−11)+29y = 2(-11) + 29.
  7. Calculate yy for x=−11x = -11: Calculate yy for x=−11x = -11: y=−22+29y = -22 + 29.
  8. Simplify to find y: Simplify to find y: y=7y = 7.
  9. Substitute x=3x = 3: Substitute x=3x = 3 into y=2x+29y = 2x + 29 to find yy: y=2(3)+29y = 2(3) + 29.
  10. Calculate yy for x=3x = 3: Calculate yy for x=3x = 3: y=6+29y = 6 + 29.
  11. Simplify to find y: Simplify to find y: y=35y = 35.
  12. Write solution as coordinate points: Write the solution as coordinate points: (−11,7)(-11, 7) and (3,35)(3, 35).

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