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Solve the system of equations.\newliney=−4x+10y = -4x + 10\newliney=x2−12x+25y = x^2 - 12x + 25\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=−4x+10y = -4x + 10\newliney=x2−12x+25y = x^2 - 12x + 25\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.−4x+10=x2−12x+25-4x + 10 = x^2 - 12x + 25
  2. Move Terms to One Side: Move all terms to one side to set the equation to zero.\newlinex2−12x+4x+25−10=0x^2 - 12x + 4x + 25 - 10 = 0\newlinex2−8x+15=0x^2 - 8x + 15 = 0
  3. Factor Quadratic Equation: Factor the quadratic equation. \newline(x−3)(x−5)=0(x - 3)(x - 5) = 0
  4. Solve for x: Solve for x by setting each factor equal to zero.\newlinex−3=0x - 3 = 0 or x−5=0x - 5 = 0\newlinex=3x = 3 or x=5x = 5
  5. Substitute x Values: Substitute x=3x = 3 into one of the original equations to find yy.\newliney=−4(3)+10y = -4(3) + 10\newliney=−12+10y = -12 + 10\newliney=−2y = -2
  6. Find y Values: Substitute x=5x = 5 into the same original equation to find y.\newliney=−4(5)+10y = -4(5) + 10\newliney=−20+10y = -20 + 10\newliney=−10y = -10
  7. Write Coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (3,−2)(3, -2)\newlineSecond Coordinate: (5,−10)(5, -10)

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