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Solve the system of equations.\newliney=x2−27x−50y = x^2 - 27x - 50\newliney=−27x+50y = -27x + 50\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=x2−27x−50y = x^2 - 27x - 50\newliney=−27x+50y = -27x + 50\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Set Equations Equal: We have the system of equations:\newliney=x2−27x−50y = x^2 - 27x - 50\newliney=−27x+50y = -27x + 50\newlineSet the two equations equal to each other to find the xx-values where they intersect.\newlinex2−27x−50=−27x+50x^2 - 27x - 50 = -27x + 50
  2. Simplify Quadratic Equation: Simplify the equation by adding 27x27x to both sides and adding 5050 to both sides to get the quadratic equation in standard form.\newlinex2−27x−50+27x+50=−27x+50+27x+50x^2 - 27x - 50 + 27x + 50 = -27x + 50 + 27x + 50\newlinex2=100x^2 = 100
  3. Solve for x: Solve for x by taking the square root of both sides.\newlinex2=100\sqrt{x^2} = \sqrt{100}\newlinex=10x = 10 or x=−10x = -10
  4. Find y-Values: Find the corresponding y-values by substituting x=10x = 10 and x=−10x = -10 into the second equation y=−27x+50y = -27x + 50. For x=10x = 10: y=−27(10)+50=−270+50=−220y = -27(10) + 50 = -270 + 50 = -220 For x=−10x = -10: y=−27(−10)+50=270+50=320y = -27(-10) + 50 = 270 + 50 = 320
  5. Write Coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (10,−220)(10, -220)\newlineSecond Coordinate: (−10,320)(-10, 320)

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