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Solve the system of equations.\newliney=−48x+96y = -48x + 96\newliney=x2−48x−48y = x^2 - 48x - 48\newline\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=−48x+96y = -48x + 96\newliney=x2−48x−48y = x^2 - 48x - 48\newline\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.−48x+96=x2−48x−48-48x + 96 = x^2 - 48x - 48
  2. Move Terms, Set to Zero: Move all terms to one side to set the equation to zero.\newline0=x2−48x+48x−48−960 = x^2 - 48x + 48x - 48 - 96
  3. Simplify Equation: Simplify the equation by combining like terms.\newline0=x2−1440 = x^2 - 144
  4. Factor Quadratic: Factor the quadratic equation.\newline0=(x−12)(x+12)0 = (x - 12)(x + 12)
  5. Solve for xx: Set each factor equal to zero and solve for xx.
    x−12=0x - 12 = 0 or x+12=0x + 12 = 0
    x=12x = 12 or x=−12x = -12
  6. Substitute xx, Find yy: Substitute x=12x = 12 into one of the original equations to find yy.y=−48(12)+96y = -48(12) + 96y=−576+96y = -576 + 96y=−480y = -480
  7. Write Coordinates: Substitute x=−12x = -12 into the same original equation to find yy.y=−48(−12)+96y = -48(-12) + 96y=576+96y = 576 + 96y=672y = 672
  8. Write Coordinates: Substitute x=−12x = -12 into the same original equation to find yy.y=−48(−12)+96y = -48(-12) + 96y=576+96y = 576 + 96y=672y = 672Write the coordinates in exact form.First Coordinate: (12,−480)\text{First Coordinate: } (12, -480)Second Coordinate: (−12,672)\text{Second Coordinate: } (-12, 672)

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