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9 Mark for Review {:[y=x+9],[y=x^(2)+16 x+63]:} A solution to the given system of equations is (x,y). What is the greatest possible value of x ? (A) -6 (B) 7 (C) 9 (D) 63

99\newlineMark for Review\newliney=x+9y=x2+16x+63 \begin{array}{c} y=x+9 \\ y=x^{2}+16 x+63 \end{array} \newlineA solution to the given system of equations is (x,y) (x, y) . What is the greatest possible value of x x ?\newline(A) −6-6\newline(B) 77\newline(C) 99\newline(D) 6363

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Q. 99\newlineMark for Review\newliney=x+9y=x2+16x+63 \begin{array}{c} y=x+9 \\ y=x^{2}+16 x+63 \end{array} \newlineA solution to the given system of equations is (x,y) (x, y) . What is the greatest possible value of x x ?\newline(A) −6-6\newline(B) 77\newline(C) 99\newline(D) 6363
  1. Set Equations Equal: Set the equations equal to each other since they both equal yy. x+9=x2+16x+63x + 9 = x^2 + 16x + 63
  2. Move Terms to One Side: Move all terms to one side to set the equation to 00. x2+16x+63−x−9=0x^2 + 16x + 63 - x - 9 = 0 x2+15x+54=0x^2 + 15x + 54 = 0
  3. Factor Quadratic Equation: Factor the quadratic equation. (x+6)(x+9)=0(x + 6)(x + 9) = 0
  4. Solve for x: Solve for xx. x+6=0x + 6 = 0 or x+9=0x + 9 = 0 x=−6x = -6 or x=−9x = -9

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