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Solve the system of equations.\newliney=−28x−6y = -28x - 6\newliney=x2−32x−38y = x^2 - 32x - 38\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Solve a system of linear and quadratic equations: parabolasright chevron icon

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Q. Solve the system of equations.\newliney=−28x−6y = -28x - 6\newliney=x2−32x−38y = x^2 - 32x - 38\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.−28x−6=x2−32x−38-28x - 6 = x^2 - 32x - 38
  2. Move Terms to One Side: Move all terms to one side to set the equation to zero.\newlinex2−32x+28x−38+6=0x^2 - 32x + 28x - 38 + 6 = 0\newlinex2−4x−32=0x^2 - 4x - 32 = 0
  3. Factor Quadratic Equation: Factor the quadratic equation.\newlinex2−4x−32=(x−8)(x+4)x^2 - 4x - 32 = (x - 8)(x + 4)
  4. Solve for x: Set each factor equal to zero and solve for x.\newline(x−8)=0(x - 8) = 0 or (x+4)=0(x + 4) = 0\newlinex=8x = 8 or x=−4x = -4
  5. Substitute xx to Find yy: Substitute xx back into one of the original equations to find yy. For x=8x = 8: y=−28(8)−6y = -28(8) - 6 which is y=−224−6y = -224 - 6 so y=−230y = -230. For x=−4x = -4: y=−28(−4)−6y = -28(-4) - 6 which is yy00 so yy11.
  6. Write Coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (8,−230)(8, -230)\newlineSecond Coordinate: (−4,106)(-4, 106)

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