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Solve the system of equations.\newliney=−5x+6y = -5x + 6\newliney=x2−5x−43y = x^2 - 5x - 43\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=−5x+6y = -5x + 6\newliney=x2−5x−43y = x^2 - 5x - 43\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=x2−5x−43y = x^2 - 5x - 43 becomes −5x+6=x2−5x−43-5x + 6 = x^2 - 5x - 43.
  2. Simplify Equation: Simplify the equation: 0=x2−5x−43+5x−60 = x^2 - 5x - 43 + 5x - 6.
  3. Combine Like Terms: Combine like terms: 0=x2−490 = x^2 - 49.
  4. Add 4949: Add 4949 to both sides: 49=x249 = x^2.
  5. Take Square Root: Take the square root of both sides: x=±7x = \pm 7.
  6. Substitute xx for yy: Substitute xx back into the first equation to find yy when x=7x = 7: y=−5(7)+6y = -5(7) + 6.
  7. Calculate y: Calculate y: y=−35+6y = -35 + 6.
  8. Simplify yy: Simplify yy: y=−29y = -29.
  9. Substitute xx for yy: Now substitute xx back into the first equation to find yy when x=−7x = -7: y=−5(−7)+6y = -5(-7) + 6.
  10. Calculate y: Calculate y: y=35+6y = 35 + 6.
  11. Simplify yy: Simplify yy: y=41y = 41.

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