8 x + 7 y = 9 24 x + 21 y = 27 For each real number r ,

Question

8 x + 7 y = 9 24 x + 21 y = 27 For each real number r , which of the following points lies on the graph of each equation in the xy -plane for the given system?

Accepted Answer

Choice A is correct. Dividing both sides of the second equation in the given system by 3 yields 8 x + 7 y = 9 , which is the first equation in the given system. Therefore, the first and second equations represent the same line in the xy -plane. If the x - and y -coordinates of a point satisfy an equation, the point lies on the graph of the equation in the xy -plane. Choice A is a point with x -coordinate r and y -coordinate - 8 r 7 + 9 7 . Substituting r for x and - 8 r 7 + 9 7 for y in the equation 8 x + 7 y = 9 yields 8 r + 7 - 8 7 r + 9 7 = 9 . Applying the distributive property to the left-hand side of this equation yields 8 r - 8 r + 9 = 9 . Combining like terms on the left-hand side of this equation yields 9 = 9 , so the coordinates of the point r , - 8 7 r + 9 7 satisfy both equations in the given system. Therefore, for each real number r , the point r , - 8 7 r + 9 7 lies on the graph of each equation in the xy -plane for the given system. 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-7-