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Solve the system of equations.\newliney=x2−21x−50y = x^2 - 21x - 50\newliney=−21x+50y = -21x + 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=x2−21x−50y = x^2 - 21x - 50\newliney=−21x+50y = -21x + 50\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.y=x2−21x−50y = x^2 - 21x - 50y=−21x+50y = -21x + 50x2−21x−50=−21x+50x^2 - 21x - 50 = -21x + 50
  2. Cancel Out Terms: Cancel out the −21x-21x on both sides.\newlinex2−21x−50+21x=−21x+50+21xx^2 - 21x - 50 + 21x = -21x + 50 + 21x\newlinex2−50=50x^2 - 50 = 50
  3. Add to Isolate x2x^2: Add 5050 to both sides to isolate x2x^2.\newlinex2−50+50=50+50x^2 - 50 + 50 = 50 + 50\newlinex2=100x^2 = 100
  4. Take Square Root: Take the square root of both sides to solve for xx.x2=100\sqrt{x^2} = \sqrt{100}x=10 or x=−10x = 10 \text{ or } x = -10
  5. Plug x=10x = 10: Plug x=10x = 10 into the second equation to find yy.y=−21(10)+50y = -21(10) + 50y=−210+50y = -210 + 50y=−160y = -160
  6. Plug x=−10x = -10: Plug x=−10x = -10 into the second equation to find yy.\newliney=−21(−10)+50y = -21(-10) + 50\newliney=210+50y = 210 + 50\newliney=260y = 260
  7. Write Coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (10,−160)(10, -160)\newlineSecond Coordinate: (−10,260)(-10, 260)

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