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Solve the system of equations.\newliney=3x2+14x−21y = 3x^2 + 14x - 21\newliney=14x+27y = 14x + 27\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newliney=3x2+14x−21y = 3x^2 + 14x - 21\newliney=14x+27y = 14x + 27\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Set Equations Equal: We have the following system of equations:\newliney=3x2+14x−21y = 3x^2 + 14x - 21\newliney=14x+27y = 14x + 27\newlineTo find the solution, we need to set the two equations equal to each other because they both equal yy.\newline3x2+14x−21=14x+273x^2 + 14x - 21 = 14x + 27
  2. Simplify by Subtracting: Subtract 14x14x from both sides to start simplifying the equation.\newline3x2+14x−21−14x=14x+27−14x3x^2 + 14x - 21 - 14x = 14x + 27 - 14x\newline3x2−21=273x^2 - 21 = 27
  3. Isolate Quadratic Term: Add 2121 to both sides to isolate the quadratic term.\newline3x2−21+21=27+213x^2 - 21 + 21 = 27 + 21\newline3x2=483x^2 = 48
  4. Solve for x2x^2: Divide both sides by 33 to solve for x2x^2.\newline3x23=483\frac{3x^2}{3} = \frac{48}{3}\newlinex2=16x^2 = 16
  5. Find xx: Take the square root of both sides to solve for xx.x2=16\sqrt{x^2} = \sqrt{16}x=4 or x=−4x = 4 \text{ or } x = -4
  6. Substitute x=4x=4: Substitute x=4x = 4 into the second equation y=14x+27y = 14x + 27 to find the corresponding y-value.\newliney=14(4)+27y = 14(4) + 27\newliney=56+27y = 56 + 27\newliney=83y = 83
  7. Substitute x=−4x=-4: Substitute x=−4x = -4 into the second equation y=14x+27y = 14x + 27 to find the corresponding y-value.\newliney=14(−4)+27y = 14(-4) + 27\newliney=−56+27y = -56 + 27\newliney=−29y = -29
  8. Write Coordinates: Write the coordinates in exact form.\newlineFor x=4x = 4, y=83y = 83, so the first coordinate is (4,83)(4, 83).\newlineFor x=−4x = -4, y=−29y = -29, so the second coordinate is (−4,−29)(-4, -29).

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