Solve the system of equations. y = 45x^2 - 6x - 20 y = -6x + 25 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

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Solve the system of equations. y = 45x^2 - 6x - 20 y = -6x + 25    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 = 45x^2 - 6x - 20 y = -6x + 25 To find the intersection points, we set the two equations equal to each other. 45x^2 - 6x - 20 = -6x + 25Simplify Equation: Now, we simplify the equation by moving all terms to one side to set the equation to zero. 45x^2 - 6x - 20 + 6x - 25 = 0 45x^2 - 45 = 0Combine Like Terms: Next, we simplify the equation further by combining like terms. 45x^2 - 45 = 0 45(x^2 - 1) = 0Factorize: We recognize that x^2 - 1 is a difference of squares, which can be factored as (x + 1)(x - 1). 45(x + 1)(x - 1) = 0Set Factors Equal: To find the values of x, we set each factor equal to zero. (x + 1) = 0 or (x - 1) = 0 Solving for x gives us x = -1 and x = 1.Find Y-Values: Now that we have the x-values, we need to find the corresponding y-values by substituting x back into one of the original equations. We can use y = -6x + 25 for simplicity. For x = -1: y = -6(-1) + 25 = 6 + 25 = 31 For x = 1: y = -6(1) + 25 = -6 + 25 = 19Coordinates: We have found the y-values corresponding to the x-values. Therefore, the coordinates of the intersection points in exact form are: First Coordinate: (-1, 31) Second Coordinate: (1, 19)

Solve the system of equations. $\newline$ $y = 45x^2 - 6x - 20$ $\newline$ $y = -6x + 25$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)

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Solve the system of equations.\newliney=45x2−6x−20y = 45x^2 - 6x - 20y=45x2−6x−20\newliney=−6x+25y = -6x + 25y=−6x+25\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

Solve the system of equations. $\newline$ $y = 45x^2 - 6x - 20$ $\newline$ $y = -6x + 25$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)