{"id":"cb_practice_pdf:t4-math-m2-q22","source_id":"cb_practice_pdf","source_item_id":"t4-math-m2-q22","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":null,"form_id":"cb_practice_pdf:test-4","module_number":2,"position":22,"stem":"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?","stimulus":"","stimulus_html":null,"stem_html":"<p>y 10 8 - 6 -1--l. -,.. - X -1 0 -8 -6 -4 -2-^&quot;-&#x27;,-- -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?</p>","rationale_html":"<p>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.</p>","correct_answer":["A"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>Zero</p>","ord":0},{"label":"B","content_html":"<p>Exactly one</p>","ord":1},{"label":"C","content_html":"<p>Exactly two</p>","ord":2},{"label":"D","content_html":"<p>Infinitely many</p>","ord":3}],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"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.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}