Solve the system of equations. y = -30x + 17 y = x^2 - 38x - 31 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

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Solve the system of equations. y = -30x + 17 y = x^2 - 38x - 31    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 = -30x + 17 y = x^2 - 38x - 31 To find the intersection points, we set the two equations equal to each other. -30x + 17 = x^2 - 38x - 31Rearrange and Solve: Rearrange the equation to bring all terms to one side and set it equal to zero to find the standard form of a quadratic equation. x^2 - 38x - 31 + 30x - 17 = 0 x^2 - 8x - 48 = 0Factor Quadratic Equation: Factor the quadratic equation to find the values of x. In quadratic equation ax^2 + bx + c, the factors are of the form (x + m)(x + n), where b is the sum and c is the product of m and n respectively. x^2 - 8x - 48 = 0 We look for two numbers that multiply to -48 and add up to -8. These numbers are -12 and 4. (x - 12)(x + 4) = 0Solve for x: Solve for x by setting each factor equal to zero. (x - 12) = 0 or (x + 4) = 0 x = 12 or x = -4Find y-Values: Find the corresponding y-values for each x-value by substituting back into one of the original equations. We can use y = -30x + 17. For x = 12: y = -30(12) + 17 y = -360 + 17 y = -343 For x = -4: y = -30(-4) + 17 y = 120 + 17 y = 137Write Coordinates: Write the coordinates in exact form. The first coordinate is (12, -343). The second coordinate is (-4, 137).

Solve the system of equations. $\newline$ $y = -30x + 17$ $\newline$ $y = x^2 - 38x - 31$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)

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Solve the system of equations.\newliney=−30x+17y = -30x + 17y=−30x+17\newliney=x2−38x−31y = x^2 - 38x - 31y=x2−38x−31\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

Solve the system of equations. $\newline$ $y = -30x + 17$ $\newline$ $y = x^2 - 38x - 31$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)