2x-3y=15 y=-(1)/(3)(x^(2)-16 x+63) If (x,y) is a solution to the system of equations shown and y 0, what is the value of x ?

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2x-3y=15  y=-(1)/(3)(x^(2)-16 x+63) If  (x,y) is a solution to the system of equations shown and  y > 0, what is the value of  x ?

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Given Equations: Given the system of equations: 1) 2x - 3y = 15 2) y = -(1/3)(x^2 - 16x + 63) We need to find the value of x for which y > 0. Let's solve the first equation for y: y = (2/3)x - 5Solving for y: Now we will substitute the expression for y from the first equation into the second equation: -(1/3)(x^2 - 16x + 63) = (2/3)x - 5Substitution and Simplification: Multiply both sides of the equation by -3 to get rid of the fractions: x^2 - 16x + 63 = -2x + 15Setting up Quadratic Equation: Now, let's move all terms to one side to set the equation to zero: x^2 - 16x + 2x + 63 - 15 = 0 x^2 - 14x + 48 = 0Factoring the Quadratic Equation: We can factor the quadratic equation: (x - 6)(x - 8) = 0Finding Possible Solutions: Setting each factor equal to zero gives us two possible solutions for x: x - 6 = 0 or x - 8 = 0 So, x = 6 or x = 8Checking Valid Solutions: We need to determine which of these solutions will give us a positive value for y. Let's substitute x = 6 into the first equation to find y: y = (2/3)(6) - 5 y = 4 - 5 y = -1 Since y is not greater than 0, x = 6 is not a valid solution.Now let's substitute x = 8 into the first equation to find y: y = (2/3)(8) - 5 y = (16/3) - 5 y = (16/3) - (15/3) y = 1/3 Since y is greater than 0, x = 8 is the valid solution.

$2 x-3 y=15$ $\newline$ $y=-\frac{1}{3}\left(x^{2}-16 x+63\right)$ $\newline$ If $(x, y)$ is a solution to the system of equations shown and y>0 , what is the value of $x$ ?

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2x−3y=15 2 x-3 y=15 2x−3y=15\newliney=−13(x2−16x+63) y=-\frac{1}{3}\left(x^{2}-16 x+63\right) y=−31​(x2−16x+63)\newlineIf (x,y) (x, y) (x,y) is a solution to the system of equations shown and y>0 , what is the value of x x x ?

$2 x-3 y=15$ $\newline$ $y=-\frac{1}{3}\left(x^{2}-16 x+63\right)$ $\newline$ If $(x, y)$ is a solution to the system of equations shown and y>0 , what is the value of $x$ ?