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Solve the system of equations.\newliney=7x−16y = 7x - 16\newliney=x2+29x+24y = x^2 + 29x + 24\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newliney=7x−16y = 7x - 16\newliney=x2+29x+24y = x^2 + 29x + 24\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 to find the xx-values where the two graphs intersect. This gives us the equation 7x−16=x2+29x+247x - 16 = x^2 + 29x + 24.
  2. Rearrange and simplify equation: Rearrange the equation to set it to zero: x2+29x+24−(7x−16)=0x^2 + 29x + 24 - (7x - 16) = 0. This simplifies to x2+22x+40=0x^2 + 22x + 40 = 0.
  3. Factor quadratic equation: Factor the quadratic equation x2+22x+40x^2 + 22x + 40. The factors of 4040 that add up to 2222 are 22 and 2020. So, the factored form is (x+2)(x+20)=0(x + 2)(x + 20) = 0.
  4. Find x-values: Set each factor equal to zero to find the x-values: x+2=0x + 2 = 0 and x+20=0x + 20 = 0. Solving these gives us x=−2x = -2 and x=−20x = -20.
  5. Substitute x=−2x = -2: Substitute x=−2x = -2 into the first equation y=7x−16y = 7x - 16 to find the corresponding y-value. This gives us y=7(−2)−16y = 7(-2) - 16, which simplifies to y=−14−16y = -14 - 16, so y=−30y = -30.
  6. Substitute x=−20x = -20: Substitute x=−20x = -20 into the first equation y=7x−16y = 7x - 16 to find the corresponding y-value. This gives us y=7(−20)−16y = 7(-20) - 16, which simplifies to y=−140−16y = -140 - 16, so y=−156y = -156.

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