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Solve the system of equations.\newliney=15x+50y = 15x + 50\newliney=x2+15x−50y = x^2 + 15x - 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=15x+50y = 15x + 50\newliney=x2+15x−50y = x^2 + 15x - 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.15x+50=x2+15x−5015x + 50 = x^2 + 15x - 50
  2. Subtract to Get Quadratic: Subtract 15x15x from both sides to get the quadratic equation.\newline50=x2−5050 = x^2 - 50
  3. Add to Isolate x2x^2: Add 5050 to both sides to isolate the x2x^2 term.\newline100=x2100 = x^2
  4. Take Square Root: Take the square root of both sides to solve for xx.x=±10x = \pm 10
  5. Plug x=10x = 10: Plug x=10x = 10 into one of the original equations to find the corresponding yy-value.\newliney=15(10)+50y = 15(10) + 50\newliney=150+50y = 150 + 50\newliney=200y = 200
  6. Plug x=−10x = -10: Plug x=−10x = -10 into one of the original equations to find the corresponding yy-value.\newliney=15(−10)+50y = 15(-10) + 50\newliney=−150+50y = -150 + 50\newliney=−100y = -100
  7. Write Coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (10,200)(10, 200)\newlineSecond Coordinate: (−10,−100)(-10, -100)

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