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Solve the system of equations.\newliney=x2−2x+37y = x^2 - 2x + 37\newliney=13x+23y = 13x + 23\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newliney=x2−2x+37y = x^2 - 2x + 37\newliney=13x+23y = 13x + 23\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: x2−2x+37=13x+23x^2 - 2x + 37 = 13x + 23.
  2. Rearrange to set to 00: Rearrange the equation to set it to 00: x2−2x−13x+37−23=0x^2 - 2x - 13x + 37 - 23 = 0.
  3. Combine like terms: Combine like terms: x2−15x+14=0x^2 - 15x + 14 = 0.
  4. Factor the quadratic equation: Factor the quadratic equation: (x−1)(x−14)=0(x - 1)(x - 14) = 0.
  5. Solve for x: Solve for x by setting each factor equal to 00: x−1=0x - 1 = 0 or x−14=0x - 14 = 0.
  6. Find first x value: Find the first value of x: x=1x = 1.
  7. Find second x value: Find the second value of x: x=14x = 14.
  8. Substitute x=1x=1 to find yy: Substitute x=1x = 1 into the first equation to find yy: y=12−2⋅1+37y = 1^2 - 2\cdot1 + 37.
  9. Calculate yy for x=1x=1: Calculate yy when x=1x = 1: y=1−2+37y = 1 - 2 + 37.
  10. Simplify to find first y: Simplify to find the first value of yy: y=36y = 36.
  11. Substitute x=14x=14 to find yy: Substitute x=14x = 14 into the first equation to find yy: y=142−2×14+37y = 14^2 - 2\times14 + 37.
  12. Calculate yy for x=14x=14: Calculate yy when x=14x = 14: y=196−28+37y = 196 - 28 + 37.
  13. Simplify to find second y: Simplify to find the second value of yy: y=205y = 205.
  14. Write coordinates of solutions: Write the coordinates of the solutions: (1,36)(1, 36) and (14,205)(14, 205).

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