y 10 8 - 6 -1--l. -,.. - X -1 0 -8 -6 -4 -2-^"-',-- -2-,-4-,--6--8- 10:2 4 6 I 18 10 1 If a new graph of three linear equations is created using the system of equations shown and the (x, y) equation x +4y = −16, how many solutions will the resulting system of three equations have?
Correct answer: A (parsed from the explanation — this source omits an answer key for this item)
Explanation
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 4x y16, this system has either zero solutions or one solution, the ( ) + =- point 8, 2. Substituting 8 for x and 2 for y in the equation 4x y16 + ( )=- =- ( ) 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 4x y16. 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.
Loading…
Searched on YouTube by topic, not by question text. Open this search on YouTube →
Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.