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Solve the system of equations.\newliney=−21x−14y = -21x - 14\newliney=x2−4x+28y = x^2 - 4x + 28\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newliney=−21x−14y = -21x - 14\newliney=x2−4x+28y = x^2 - 4x + 28\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute yy into second equation: Substitute yy from the first equation into the second equation: y=x2−4x+28y = x^2 - 4x + 28 becomes −21x−14=x2−4x+28-21x - 14 = x^2 - 4x + 28.
  2. Rearrange to set to 00: Rearrange the equation to set it to 00: x2−4x+28+21x+14=0x^2 - 4x + 28 + 21x + 14 = 0, which simplifies to x2+17x+42=0x^2 + 17x + 42 = 0.
  3. Factor the quadratic equation: Factor the quadratic equation: (x+7)(x+6)=0(x + 7)(x + 6) = 0.
  4. Solve for x: Solve for x by setting each factor equal to 00: x+7=0x + 7 = 0 or x+6=0x + 6 = 0.
  5. Find first x value: Find the first value of x: x=−7x = -7.
  6. Find second x value: Find the second value of x: x=−6x = -6.
  7. Substitute x=−7x=-7 for yy: Substitute x=−7x = -7 into the first equation to find yy: y=−21(−7)−14y = -21(-7) - 14.
  8. Calculate yy for x=−7x=-7: Calculate yy for x=−7x = -7: y=147−14y = 147 - 14, which simplifies to y=133y = 133.
  9. Substitute x=−6x=-6 for yy: Substitute x=−6x = -6 into the first equation to find yy: y=−21(−6)−14y = -21(-6) - 14.
  10. Calculate yy for x=−6x=-6: Calculate yy for x=−6x = -6: y=126−14y = 126 - 14, which simplifies to y=112y = 112.
  11. Write solution as coordinate points: Write the solution as coordinate points: (−7,133)(-7, 133) and (−6,112)(-6, 112).

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