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Solve the system of equations.\newliney=39x+32y = 39x + 32\newliney=x2+39x−17y = x^2 + 39x - 17\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=39x+32y = 39x + 32\newliney=x2+39x−17y = x^2 + 39x - 17\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Set Equations Equal: Since both equations equal yy, set them equal to each other: 39x+32=x2+39x−1739x + 32 = x^2 + 39x - 17.
  2. Subtract 39x39x: Subtract 39x39x from both sides to get: 32=x2−1732 = x^2 - 17.
  3. Add 1717: Add 1717 to both sides to find xx: x2=49x^2 = 49.
  4. Take Square Root: Take the square root of both sides to solve for xx: x=±7x = \pm 7.
  5. Plug x=7x = 7: Plug x=7x = 7 into the first equation to find yy: y=39(7)+32y = 39(7) + 32.
  6. Calculate y: Calculate y: y=273+32=305y = 273 + 32 = 305.
  7. Plug x=−7x = -7: Now plug x=−7x = -7 into the first equation to find yy: y=39(−7)+32y = 39(-7) + 32.
  8. Calculate y: Calculate y: y=−273+32=−241y = -273 + 32 = -241.

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