Solve the system of equations. y = -42x + 50 y = x^2 - 42x - 50 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

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Solve the system of equations. y = -42x + 50 y = x^2 - 42x - 50    Write the coordinates in exact form. Simplify all fractions and radicals.  (______,______) (______,______)

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Set Equations Equal: We have the system of equations: y = -42x + 50 y = x^2 - 42x - 50 To find the solution, we will set the two equations equal to each other since they both equal y. -42x + 50 = x^2 - 42x - 50Simplify and Rearrange: Now we simplify the equation by moving all terms to one side to set the equation to zero. -42x + 50 - (-42x) - 50 = x^2 - 42x - 50 - (-42x) - 50 0 = x^2 - 50Solve Quadratic Equation: We now have a simple quadratic equation: x^2 - 50 = 0 To solve for x, we can add 50 to both sides of the equation. x^2 = 50Find x-values: Next, we take the square root of both sides to solve for x. x = sqrt(50) or x = -sqrt(50) Since sqrt(50) can be simplified to 5*sqrt(2), we have: x = 5*sqrt(2) or x = -5*sqrt(2)Substitute x-values: We now have two possible values for x. We need to find the corresponding y-values for each x-value by substituting them back into one of the original equations. We can use the simpler equation y = -42x + 50. First, let's substitute x = 5*sqrt(2): y = -42*(5*sqrt(2)) + 50 y = -210*sqrt(2) + 50Final Coordinates: Now let's substitute x = -5*sqrt(2): y = -42*(-5*sqrt(2)) + 50 y = 210*sqrt(2) + 50We now have the two sets of coordinates in exact form: First Coordinate: (5*sqrt(2), -210*sqrt(2) + 50) Second Coordinate: (-5*sqrt(2), 210*sqrt(2) + 50)

Solve the system of equations. $\newline$ $y = -42x + 50$ $\newline$ $y = x^2 - 42x - 50$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)

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Solve the system of equations.\newliney=−42x+50y = -42x + 50y=−42x+50\newliney=x2−42x−50y = x^2 - 42x - 50y=x2−42x−50\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

Solve the system of equations. $\newline$ $y = -42x + 50$ $\newline$ $y = x^2 - 42x - 50$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)