For the first line in the system: The line slants gradually down from left to right. The line passes through

Question

If a new graph of three linear equations is created using the system of equations shown and the equation $x + 4 y = - 16$ , how many solutions $(x, y)$ will the resulting system of three equations have?

Accepted Answer

Choice A is correct. A solution to a system of equations must satisfy each equation in the system. It follows that if an ordered pair x , y is a solution to the system, the point x , y lies on the graph in the xy -plane of each equation in the system. The only point that lies on each graph of the system of two linear equations shown is their intersection point 8 , 2 . It follows that if a new graph of three linear equations is created using the system of equations shown and the graph of x + 4 y = - 16 , this system has either zero solutions or one solution, the point 8 , 2 . Substituting 8 for x and 2 for y in the equation x + 4 y = - 16 yields 8 + 4 2 = - 16 , or 16 = - 16 . Since this equation is not true, the point 8 , 2 does not lie on the graph of x + 4 y = - 16 . Therefore, 8 , 2 is not a solution to the system of three equations. It follows that there are zero solutions to this 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.

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