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Solve the system of equations.\newliney=50x−33y = 50x - 33\newliney=x2+32x−1y = x^2 + 32x - 1\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newliney=50x−33y = 50x - 33\newliney=x2+32x−1y = x^2 + 32x - 1\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Set Equations Equal: Since both equations are equal to yy, we can set them equal to each other to find xx. This gives us the equation 50x−33=x2+32x−150x - 33 = x^2 + 32x - 1.
  2. Rearrange and Solve: Rearrange the equation to set it to zero and solve for xx. This means we subtract 50x−3350x - 33 from both sides to get 0=x2+32x−50x−1+330 = x^2 + 32x - 50x - 1 + 33, which simplifies to 0=x2−18x+320 = x^2 - 18x + 32.
  3. Factor Quadratic Equation: Factor the quadratic equation x2−18x+32=0x^2 - 18x + 32 = 0. The factors of 3232 that add up to −18-18 are −16-16 and −2-2. So the factored form is (x−16)(x−2)=0(x - 16)(x - 2) = 0.
  4. Solve for x: Solve for x by setting each factor equal to zero. This gives us x−16=0x - 16 = 0 or x−2=0x - 2 = 0, which means x=16x = 16 or x=2x = 2.
  5. Substitute x Values: Substitute x=16x = 16 into one of the original equations to find yy. Using y=50x−33y = 50x - 33, we get y=50(16)−33y = 50(16) - 33, which simplifies to y=800−33y = 800 - 33, giving us y=767y = 767.
  6. Find y Values: Substitute x=2x = 2 into the same equation to find the other value of yy. Using y=50x−33y = 50x - 33, we get y=50(2)−33y = 50(2) - 33, which simplifies to y=100−33y = 100 - 33, giving us y=67y = 67.
  7. Write Coordinate Points: Write the solution as coordinate points. The coordinate points are (16,767)(16, 767) and (2,67)(2, 67).

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