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Solve the system of equations.\newliney=−47x+5y = -47x + 5\newliney=3x2−47x−43y = 3x^2 - 47x - 43\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newliney=−47x+5y = -47x + 5\newliney=3x2−47x−43y = 3x^2 - 47x - 43\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Set Equations Equal: Set the two equations equal to each other since they both equal yy.y=−47x+5y = -47x + 5y=3x2−47x−43y = 3x^2 - 47x - 43So, −47x+5=3x2−47x−43-47x + 5 = 3x^2 - 47x - 43.
  2. Simplify Equation: Simplify the equation by moving all terms to one side to set the equation to zero.\newline0=3x2−47x+47x−43−50 = 3x^2 - 47x + 47x - 43 - 5\newline0=3x2−480 = 3x^2 - 48
  3. Solve for x: Solve for x by adding 4848 to both sides and then dividing by 33. \newline3x2=483x^2 = 48\newlinex2=483x^2 = \frac{48}{3}\newlinex2=16x^2 = 16
  4. Take Square Root: Take the square root of both sides to solve for xx.x=±16x = \pm\sqrt{16}x=±4x = \pm4
  5. Substitute xx: Substitute x=4x = 4 into one of the original equations to solve for yy. Using y=−47x+5y = -47x + 5, we get: y=−47(4)+5y = -47(4) + 5 y=−188+5y = -188 + 5 y=−183y = -183
  6. Coordinate Points: Substitute x=−4x = -4 into the same equation to solve for yy.y=−47(−4)+5y = -47(-4) + 5y=188+5y = 188 + 5y=193y = 193
  7. Coordinate Points: Substitute x=−4x = -4 into the same equation to solve for yy.y=−47(−4)+5y = -47(-4) + 5y=188+5y = 188 + 5y=193y = 193Write the solution as coordinate points.The coordinate points are (4,−183)(4, -183) and (−4,193)(-4, 193).

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