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Solve the system of equations.\newliney=21x−36y = 21x - 36\newliney=x2+9x−1y = x^2 + 9x - 1\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=21x−36y = 21x - 36\newliney=x2+9x−1y = x^2 + 9x - 1\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. Since y=21x−36y = 21x - 36 and y=x2+9x−1y = x^2 + 9x - 1, we can set them equal to each other: 21x−36=x2+9x−121x - 36 = x^2 + 9x - 1.
  2. Rearrange and Solve: Rearrange the equation to set it to zero and solve for xx: x2+9x−1−21x+36=0x^2 + 9x - 1 - 21x + 36 = 0, which simplifies to x2−12x+35=0x^2 - 12x + 35 = 0.
  3. Factor Quadratic Equation: Factor the quadratic equation: (x−7)(x−5)=0(x - 7)(x - 5) = 0.
  4. Solve for x: Solve for x by setting each factor equal to zero: x−7=0x - 7 = 0 or x−5=0x - 5 = 0. This gives us two solutions for xx: x=7x = 7 and x=5x = 5.
  5. Substitute x=7x = 7: Substitute x=7x = 7 into the first equation y=21x−36y = 21x - 36 to find the corresponding value of yy: y=21(7)−36y = 21(7) - 36, which simplifies to y=147−36y = 147 - 36, so y=111y = 111.
  6. Substitute x=5x = 5: Substitute x=5x = 5 into the first equation y=21x−36y = 21x - 36 to find the corresponding value of yy: y=21(5)−36y = 21(5) - 36, which simplifies to y=105−36y = 105 - 36, so y=69y = 69.
  7. Write Coordinate Points: Write the solution as coordinate points. The coordinate points are (7,111)(7, 111) and (5,69)(5, 69).

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