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Solve the system of equations.\newliney=9x2−15x−33y = 9x^2 - 15x - 33\newliney=−15x+3y = -15x + 3\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=9x2−15x−33y = 9x^2 - 15x - 33\newliney=−15x+3y = -15x + 3\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.9x2−15x−33=−15x+39x^2 - 15x - 33 = -15x + 3
  2. Move Terms to One Side: Move all terms to one side to set the equation to zero.\newline9x2−15x−33+15x−3=09x^2 - 15x - 33 + 15x - 3 = 0\newline9x2−36=09x^2 - 36 = 0
  3. Factor Quadratic Equation: Factor the quadratic equation.\newline9(x2−4)=09(x^2 - 4) = 0\newline9(x−2)(x+2)=09(x - 2)(x + 2) = 0
  4. Solve for x: Set each factor equal to zero and solve for x.\newlinex−2=0x - 2 = 0 or x+2=0x + 2 = 0\newlinex=2x = 2 or x=−2x = -2
  5. Substitute x Values: Substitute xx values into the second equation to find yy values.\newlineFor x=2x = 2: y=−15(2)+3=−30+3=−27y = -15(2) + 3 = -30 + 3 = -27\newlineFor x=−2x = -2: y=−15(−2)+3=30+3=33y = -15(-2) + 3 = 30 + 3 = 33
  6. Write Coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (2,−27)(2, -27)\newlineSecond Coordinate: (−2,33)(-2, 33)

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