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Solve the system of equations.\newliney=x2+36x+3 y = x^2 + 36x + 3 \newliney=22x37 y = 22x - 37 \newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(_,_)(\_,\_)\newline(_,_)(\_,\_)

Full solution

Q. Solve the system of equations.\newliney=x2+36x+3 y = x^2 + 36x + 3 \newliney=22x37 y = 22x - 37 \newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(_,_)(\_,\_)\newline(_,_)(\_,\_)
  1. Set up quadratic equation: Now, subtract 22x22x and add 3737 to both sides to get the quadratic equation.\newlinex2+36x+322x+37=0x^2 + 36x + 3 - 22x + 37 = 0\newlinex2+14x+40=0x^2 + 14x + 40 = 0
  2. Factor the equation: Next, factor the quadratic equation. \newline(x+10)(x+4)=0(x + 10)(x + 4) = 0
  3. Solve for xx: Then, solve for xx by setting each factor equal to zero.\newlinex+10=0x + 10 = 0 or x+4=0x + 4 = 0\newlinex=10x = -10 or x=4x = -4
  4. Find y values: Now, plug x values into one of the original equations to find y.\newlineFor x=10x = -10: y=22(10)37=22037=257y = 22(-10) - 37 = -220 - 37 = -257\newlineFor x=4x = -4: y=22(4)37=8837=125y = 22(-4) - 37 = -88 - 37 = -125
  5. Write coordinates: Finally, write the coordinates in exact form.\newlineFirst Coordinate: (10,257)(-10, -257)\newlineSecond Coordinate: (4,125)(-4, -125)

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