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Solve the system of equations.\newliney=7x+100y = 7x + 100\newliney=x2+7x−44y = x^2 + 7x - 44\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=7x+100y = 7x + 100\newliney=x2+7x−44y = x^2 + 7x - 44\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+7x−44y = x^2 + 7x - 44 becomes 7x+100=x2+7x−447x + 100 = x^2 + 7x - 44.
  2. Solve for x: Subtract 7x7x from both sides to get 100=x2−44100 = x^2 - 44.
  3. Find xx: Add 4444 to both sides to get x2=144x^2 = 144.
  4. Calculate yy for x=12x = 12: Take the square root of both sides to find xx. This gives us x=12x = 12 and x=−12x = -12, since both 12212^2 and (−12)2(-12)^2 equal 144144.
  5. Calculate yy for x=−12x = -12: Plug x=12x = 12 into the first equation y=7x+100y = 7x + 100 to find the corresponding yy value. This gives us y=7(12)+100y = 7(12) + 100.
  6. Calculate yy for x=−12x = -12: Plug x=12x = 12 into the first equation y=7x+100y = 7x + 100 to find the corresponding yy value. This gives us y=7(12)+100y = 7(12) + 100.Calculate yy for x=12x = 12. y=84+100y = 84 + 100, which is y=184y = 184.
  7. Calculate yy for x=−12x = -12: Plug x=12x = 12 into the first equation y=7x+100y = 7x + 100 to find the corresponding yy value. This gives us y=7(12)+100y = 7(12) + 100.Calculate yy for x=12x = 12. y=84+100y = 84 + 100, which is y=184y = 184.Now plug x=−12x = -12 into the first equation y=7x+100y = 7x + 100 to find the corresponding yy value. This gives us x=−12x = -1233.
  8. Calculate yy for x=−12x = -12: Plug x=12x = 12 into the first equation y=7x+100y = 7x + 100 to find the corresponding yy value. This gives us y=7(12)+100y = 7(12) + 100.Calculate yy for x=12x = 12. y=84+100y = 84 + 100, which is y=184y = 184.Now plug x=−12x = -12 into the first equation y=7x+100y = 7x + 100 to find the corresponding yy value. This gives us x=−12x = -1233.Calculate yy for x=−12x = -12. x=−12x = -1266, which is x=−12x = -1277.

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