{:[y=x^(2)+6x-18],[y=2x+3]:} Which of the following is a solution to the system of equations? Choose 1 answer: (A) (-5,-23) (B) (1,-11) (c) (2,7) (D) (3,9)

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{:[y=x^(2)+6x-18],[y=2x+3]:} Which of the following is a solution to the system of equations? Choose 1 answer: (A)  (-5,-23) (B)  (1,-11) (c)  (2,7) (D)  (3,9)

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Substitution Method: To solve the system of equations, we can use substitution or elimination. Since one of the equations is already solved for y, substitution is the most straightforward method. We will substitute the expression for y from the second equation, y = 2x + 3, into the first equation, y = x^2 + 6x - 18.Substitute y into first equation: Substitute y = 2x + 3 into the first equation: 2x + 3 = x^2 + 6x - 18Rearrange and solve for x: Rearrange the equation to set it to zero and solve for x: x^2 + 6x - 18 - (2x + 3) = 0 x^2 + 6x - 2x - 18 - 3 = 0 x^2 + 4x - 21 = 0Factor the quadratic equation: Factor the quadratic equation: (x + 7)(x - 3) = 0Solve for x: Set each factor equal to zero and solve for x: x + 7 = 0 or x - 3 = 0 x = -7 or x = 3Substitute x=-7 and x=3 into y: We have two possible x-values: x = -7 and x = 3. We will substitute these values back into the second equation, y = 2x + 3, to find the corresponding y-values.Substitute x=-7 into y: First, substitute x = -7 into y = 2x + 3: y = 2(-7) + 3 y = -14 + 3 y = -11Check x=-7, y=-11: The pair (-7, -11) is not one of the answer choices, so we will check the second x-value.Substitute x=3 into y: Now, substitute x = 3 into y = 2x + 3: y = 2(3) + 3 y = 6 + 3 y = 9Check x=3, y=9: The pair (3, 9) is one of the answer choices, so we will check if it is the correct solution to the system of equations.Verify solution: We will substitute x = 3 and y = 9 into the first equation to verify if it satisfies the equation: 9 = (3)^2 + 6(3) - 18 9 = 9 + 18 - 18 9 = 9Since the pair (3, 9) satisfies both equations in the system, it is the correct solution.

$y=x^{2}+6 x-18$ $\newline$ $y=2 x+3$ $\newline$ Which of the following is a solution to the system of equations? $\newline$ Choose $1$ answer: $\newline$ (A) $(-5,-23)$ $\newline$ (B) $(1,-11)$ $\newline$ (C) $(2,7)$ $\newline$ (D) $(3,9)$

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