y = x + 9 y = x 2 + 16 x + 63 A solution to the given system

Question

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 ?

Accepted Answer

Choice A is correct. It's given that y = x + 9 and y = x 2 + 16 x + 63 ; therefore, it follows that x + 9 = x 2 + 16 x + 63 . This equation can be rewritten as x + 9 = x + 9 x + 7 . Subtracting x + 9 from both sides of this equation yields 0 = x + 9 x + 7 - x + 9 . This equation can be rewritten as 0 = x + 9 x + 7 - 1 , or 0 = x + 9 x + 6 . By the zero product property, x + 9 = 0 or x + 6 = 0 . Subtracting 9 from both sides of the equation x + 9 = 0 yields x = - 9 . Subtracting 6 from both sides of the equation x + 6 = 0 yields x = - 6 . Therefore, the given system of equations has solutions, x , y , that occur when x = - 9 and x = - 6 . Since - 6 is greater than - 9 , the greatest possible value of x is - 6 . Choice B is incorrect. This is the negative of the greatest possible value of x when y = 0 for the second equation in the given system of equations. Choice C is incorrect. This is the value of y when x = 0 for the first equation in the given system of equations. Choice D is incorrect. This is the value of y when x = 0 for the second equation in the given system of equations.

Question y-x-9-