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Solve the system of equations.\newliney=x2−38x−50y = x^2 - 38x - 50\newliney=−38x+50y = -38x + 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=x2−38x−50y = x^2 - 38x - 50\newliney=−38x+50y = -38x + 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=x2−38x−50y = x^2 - 38x - 50y=−38x+50y = -38x + 50x2−38x−50=−38x+50x^2 - 38x - 50 = -38x + 50
  2. Cancel Out Terms: Cancel out the −38x-38x on both sides.\newlinex2−38x−50+38x=−38x+50+38xx^2 - 38x - 50 + 38x = -38x + 50 + 38x\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. Substitute xx for yy: Substitute xx back into one of the original equations to find yy.\newlineFor x=10x = 10: y=−38(10)+50y = -38(10) + 50\newliney=−380+50y = -380 + 50\newliney=−330y = -330
  6. Substitute xx Again: Substitute xx back into one of the original equations to find yy for the second value of xx.\newlineFor x=−10x = -10: y=−38(−10)+50y = -38(-10) + 50\newliney=380+50y = 380 + 50\newliney=430y = 430
  7. Write Coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (10,−330)(10, -330)\newlineSecond Coordinate: (−10,430)(-10, 430)

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