Solve the system of equations. y = x^2 - 11x + 27 y = -22x + 3 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

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Solve the system of equations. y = x^2 - 11x + 27 y = -22x + 3    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 = x^2 - 11x + 27 y = -22x + 3 To find the solution, we will set the two equations equal to each other because they both equal y. x^2 - 11x + 27 = -22x + 3Rearrange and Standardize: Now we will rearrange the equation to bring all terms to one side and set it equal to zero, which will give us a standard form of a quadratic equation. x^2 - 11x + 27 + 22x - 3 = 0 Combining like terms, we get: x^2 + 11x + 24 = 0Factor Quadratic Equation: Next, we need to factor the quadratic equation. We are looking for two numbers that multiply to 24 and add up to 11. These numbers are 8 and 3. So we can write the factored form as: (x + 8)(x + 3) = 0Solve for x: Now we will solve for x by setting each factor equal to zero. First, for (x + 8) = 0, we get x = -8. Second, for (x + 3) = 0, we get x = -3.Find y-values: With the x-values found, we now need to find the corresponding y-values. We can substitute x back into either of the original equations. We'll use the second equation y = -22x + 3 for simplicity. For x = -8, we substitute into the equation to get y = -22(-8) + 3 = 176 + 3 = 179. For x = -3, we substitute into the equation to get y = -22(-3) + 3 = 66 + 3 = 69.

Solve the system of equations. $\newline$ $y = x^2 - 11x + 27$ $\newline$ $y = -22x + 3$ $\newline$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)

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Solve the system of equations.\newliney=x2−11x+27y = x^2 - 11x + 27y=x2−11x+27\newliney=−22x+3y = -22x + 3y=−22x+3\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

Solve the system of equations. $\newline$ $y = x^2 - 11x + 27$ $\newline$ $y = -22x + 3$ $\newline$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)