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Solve the system of equations.\newliney=x2+x+50y = x^2 + x + 50\newliney=21x−50y = 21x - 50\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\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+x+50y = x^2 + x + 50\newliney=21x−50y = 21x - 50\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)
  1. Set Equations Equal: Set the two equations equal to each other since they both equal yy.y=x2+x+50y = x^2 + x + 50y=21x−50y = 21x - 50x2+x+50=21x−50x^2 + x + 50 = 21x - 50
  2. Subtract and Simplify: Subtract 21x21x from both sides to get the quadratic equation.\newlinex2+x+50−21x=21x−50−21xx^2 + x + 50 - 21x = 21x - 50 - 21x\newlinex2−20x+50+50=0x^2 - 20x + 50 + 50 = 0\newlinex2−20x+100=0x^2 - 20x + 100 = 0
  3. Factor Quadratic Equation: Factor the quadratic equation. \newline(x−10)2=0(x - 10)^2 = 0
  4. Solve for x: Solve for x by taking the square root of both sides.\newlinex−10=0x - 10 = 0\newlinex=10x = 10
  5. Substitute and Find yy: Substitute xx back into one of the original equations to find yy. Using y=21x−50y = 21x - 50: y=21(10)−50y = 21(10) - 50 y=210−50y = 210 - 50 y=160y = 160
  6. Write Coordinates: Write the coordinates in exact form.\newlineThe solution to the system of equations is (10,160)(10, 160).

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