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Solve the system of equations.\newliney=3x−44y = 3x - 44\newliney=x2−15x−12y = x^2 - 15x - 12\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Solve a nonlinear system of equationsright chevron icon

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Q. Solve the system of equations.\newliney=3x−44y = 3x - 44\newliney=x2−15x−12y = x^2 - 15x - 12\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute y Equation: Substitute yy from the first equation into the second equation: y=x2−15x−12y = x^2 - 15x - 12 becomes 3x−44=x2−15x−123x - 44 = x^2 - 15x - 12.
  2. Rearrange to Set to 00: Rearrange the equation to set it to 00: x2−15x−12−3x+44=0x^2 - 15x - 12 - 3x + 44 = 0, which simplifies to x2−18x+32=0x^2 - 18x + 32 = 0.
  3. Factor Quadratic Equation: Factor the quadratic equation: (x−16)(x−2)=0(x - 16)(x - 2) = 0.
  4. Solve for x: Solve for x: x=16x = 16 or x=2x = 2.
  5. Substitute x=16x = 16: Substitute x=16x = 16 into the first equation to find yy: y=3(16)−44y = 3(16) - 44, y=48−44y = 48 - 44, y=4y = 4.
  6. Substitute x=2x = 2: Substitute x=2x = 2 into the first equation to find yy: y=3(2)−44y = 3(2) - 44, y=6−44y = 6 - 44, y=−38y = -38.

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