{:[x=2y+5],[y=(2x-3)(x+9)]:} How many ordered pairs (x,y) satisfy the system of equations shown above? A) 0 B) 1 C) 2 D) Infinitely many

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{:[x=2y+5],[y=(2x-3)(x+9)]:} How many ordered pairs  (x,y) satisfy the system of equations shown above? A) 0 B) 1 C) 2 D) Infinitely many

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Understand the Equations: Understand the system of equations. We have a system of two equations: 1) x = 2y + 5 2) y = (2x - 3)(x + 9) We need to find the number of ordered pairs (x, y) that satisfy both equations simultaneously.Substitute and Solve: Substitute the expression for x from the first equation into the second equation. From equation 1, we have x = 2y + 5. We can substitute this into equation 2 in place of x to solve for y. y = (2(2y + 5) - 3)((2y + 5) + 9)Simplify the Expression: Simplify the equation obtained after substitution. y = (4y + 10 - 3)(2y + 14) y = (4y + 7)(2y + 14) Now, we will expand this to get a quadratic equation in terms of y.Expand and Simplify: Expand the equation and simplify. y = (4y + 7)(2y + 14) y = 8y^2 + 28y + 14y + 98 y = 8y^2 + 42y + 98Set Equation to Zero: Move all terms to one side to set the equation to zero. 0 = 8y^2 + 42y + 98 - y 0 = 8y^2 + 41y + 98Factor Quadratic Equation: Factor the quadratic equation, if possible. We need to factor 8y^2 + 41y + 98. However, this does not factor nicely, and we may need to use the quadratic formula to find the roots.Use Quadratic Formula: Use the quadratic formula to find the roots of the equation. The quadratic formula is y = (-b ± √(b^2 - 4ac)) / (2a), where a = 8, b = 41, and c = 98. Discriminant = b^2 - 4ac = 41^2 - 4(8)(98) Discriminant = 1681 - 3136 Discriminant = -1455Analyzing the Discriminant: Analyze the discriminant. Since the discriminant is negative (-1455), there are no real solutions for y. This means there are no ordered pairs (x, y) that satisfy the system of equations.

$\begin{array}{l} x=2 y+5 \\ y=(2 x-3)(x+9) \end{array}$ $\newline$ How many ordered pairs $(x, y)$ satisfy the system of equations shown above? $\newline$ A) $0$ $\newline$ B) $1$ $\newline$ C) $2$ $\newline$ D) Infinitely many

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x=2y+5y=(2x−3)(x+9) \begin{array}{l} x=2 y+5 \\ y=(2 x-3)(x+9) \end{array} x=2y+5y=(2x−3)(x+9)​\newlineHow many ordered pairs (x,y) (x, y) (x,y) satisfy the system of equations shown above?\newlineA) 000\newlineB) 111\newlineC) 222\newlineD) Infinitely many

$\begin{array}{l} x=2 y+5 \\ y=(2 x-3)(x+9) \end{array}$ $\newline$ How many ordered pairs $(x, y)$ satisfy the system of equations shown above? $\newline$ A) $0$ $\newline$ B) $1$ $\newline$ C) $2$ $\newline$ D) Infinitely many