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Solve the system of equations.\newliney=−2x+6y = -2x + 6\newliney=x2−14x+42y = x^2 - 14x + 42\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)

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Q. Solve the system of equations.\newliney=−2x+6y = -2x + 6\newliney=x2−14x+42y = x^2 - 14x + 42\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)
  1. Substitute yy Equation: Substitute yy from the first equation into the second equation: y=x2−14x+42y = x^2 - 14x + 42 becomes −2x+6=x2−14x+42-2x + 6 = x^2 - 14x + 42.
  2. Rearrange to Set 00: Rearrange the equation to set it to 00: x2−14x+42+2x−6=0x^2 - 14x + 42 + 2x - 6 = 0, which simplifies to x2−12x+36=0x^2 - 12x + 36 = 0.
  3. Factor Quadratic Equation: Factor the quadratic equation: (x−6)(x−6)=0(x - 6)(x - 6) = 0.
  4. Solve for x: Solve for x: x−6=0x - 6 = 0, so x=6x = 6.
  5. Substitute xx for yy: Substitute xx back into the first equation to find yy: y=−2(6)+6y = -2(6) + 6, which simplifies to y=−12+6y = -12 + 6.
  6. Calculate y: Calculate y: y=−6y = -6.

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