8 x + y = - 11 2 x 2 = y + 341 The graphs of the equations in

Question

8 x + y = - 11 2 x 2 = y + 341 The graphs of the equations in the given system of equations intersect at the point ( x , y ) in the x y -plane. What is a possible value of x ?

Accepted Answer

Choice A is correct. It's given that the graphs of the equations in the given system of equations intersect at the point x , y . Therefore, this intersection point is a solution to the given system. The solution can be found by isolating y in each equation. The given equation 8 x + y = - 11 can be rewritten to isolate y by subtracting 8 x from both sides of the equation, which gives y = - 8 x - 11 . The given equation 2 x 2 = y + 341 can be rewritten to isolate y by subtracting 341 from both sides of the equation, which gives 2 x 2 - 341 = y . With each equation solved for y , the value of y from one equation can be substituted into the other, which gives 2 x 2 - 341 = - 8 x - 11 . Adding 8 x and 11 to both sides of this equation results in 2 x 2 + 8 x - 330 = 0 . Dividing both sides of this equation by 2 results in x 2 + 4 x - 165 = 0 . This equation can be rewritten by factoring the left-hand side, which yields x + 15 x - 11 = 0 . By the zero-product property, if x + 15 x - 11 = 0 , then x + 15 = 0 , or x - 11 = 0 . It follows that x = - 15 , or x = 11 . Since only - 15 is given as a choice, a possible value of x is - 15 . Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

Question 8-x-y-