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Solve the system of equations.\newliney=−46x+41y = -46x + 41\newliney=x2−46x−40y = x^2 - 46x - 40\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=−46x+41y = -46x + 41\newliney=x2−46x−40y = x^2 - 46x - 40\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.−46x+41=x2−46x−40-46x + 41 = x^2 - 46x - 40
  2. Move Terms to One Side: Move all terms to one side to set the equation to zero.\newlinex2−46x+46x−40−41=0x^2 - 46x + 46x - 40 - 41 = 0\newlinex2−81=0x^2 - 81 = 0
  3. Factor Quadratic Equation: Factor the quadratic equation. \newline(x−9)(x+9)=0(x - 9)(x + 9) = 0
  4. Solve for x: Solve for x by setting each factor equal to zero.\newlinex−9=0x - 9 = 0 or x+9=0x + 9 = 0\newlinex=9x = 9 or x=−9x = -9
  5. Substitute x=9x = 9: Substitute x=9x = 9 into one of the original equations to find yy.\newliney=−46(9)+41y = -46(9) + 41\newliney=−414+41y = -414 + 41\newliney=−373y = -373
  6. Substitute x=−9x = -9: Substitute x=−9x = -9 into the same original equation to find the other yy.y=−46(−9)+41y = -46(-9) + 41y=414+41y = 414 + 41y=455y = 455

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