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Solve the system of equations.\newliney=3x+16y = 3x + 16\newliney=x2+x−19y = x^2 + x - 19\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)\newline

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Q. Solve the system of equations.\newliney=3x+16y = 3x + 16\newliney=x2+x−19y = x^2 + x - 19\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)\newline
  1. Substitute yy into second equation: Substitute yy from the first equation into the second equation, so we have 3x+16=x2+x−193x + 16 = x^2 + x - 19.
  2. Rearrange to set to 00: Rearrange the equation to set it to 00: x2+x−19−3x−16=0x^2 + x - 19 - 3x - 16 = 0, which simplifies to x2−2x−35=0x^2 - 2x - 35 = 0.
  3. Factor the quadratic equation: Factor the quadratic equation: (x−7)(x+5)=0(x - 7)(x + 5) = 0.
  4. Solve for x: Solve for x by setting each factor equal to 00: x−7=0x - 7 = 0 or x+5=0x + 5 = 0.
  5. Find values of x: Find the two values of xx: x=7x = 7 and x=−5x = -5.
  6. Substitute x=7x=7 for yy: Substitute x=7x = 7 into the first equation y=3x+16y = 3x + 16 to find the corresponding yy value: y=3(7)+16y = 3(7) + 16.
  7. Calculate yy for x=7x=7: Calculate yy when x=7x = 7: y=21+16y = 21 + 16, which gives y=37y = 37.
  8. Substitute x=−5x=-5 for yy: Substitute x=−5x = -5 into the first equation y=3x+16y = 3x + 16 to find the corresponding yy value: y=3(−5)+16y = 3(-5) + 16.
  9. Calculate yy for x=−5x=-5: Calculate yy when x=−5x = -5: y=−15+16y = -15 + 16, which gives y=1y = 1.
  10. Write solutions as coordinate points: Write the solutions as coordinate points: (7,37)(7, 37) and (−5,1)(-5, 1).

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