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Solve the system of equations.\newliney=x2+20x−25y = x^2 + 20x - 25\newliney=22x+23y = 22x + 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+20x−25y = x^2 + 20x - 25\newliney=22x+23y = 22x + 23\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.x2+20x−25=22x+23x^2 + 20x - 25 = 22x + 23
  2. Subtract and Simplify: Subtract 22x+2322x + 23 from both sides to set the equation to zero.\newlinex2+20x−25−22x−23=0x^2 + 20x - 25 - 22x - 23 = 0
  3. Combine Like Terms: Combine like terms.\newlinex2−2x−48=0x^2 - 2x - 48 = 0
  4. Factor Quadratic Equation: Factor the quadratic equation. \newline(x−8)(x+6)=0(x - 8)(x + 6) = 0
  5. Solve for xx: Set each factor equal to zero and solve for xx.x−8=0x - 8 = 0 and x+6=0x + 6 = 0x=8x = 8 and x=−6x = -6
  6. Substitute x=8x = 8: Substitute x=8x = 8 into the first equation to find yy.y=82+20(8)−25y = 8^2 + 20(8) - 25y=64+160−25y = 64 + 160 - 25y=199y = 199
  7. Substitute x=−6x = -6: Substitute x=−6x = -6 into the first equation to find yy.\newliney=(−6)2+20(−6)−25y = (-6)^2 + 20(-6) - 25\newliney=36−120−25y = 36 - 120 - 25\newliney=−109y = -109
  8. Write Coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (8,199)(8, 199)\newlineSecond Coordinate: (−6,−109)(-6, -109)

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