{"id":"cb_practice_pdf:t11-math-m1-q25","source_id":"cb_practice_pdf","source_item_id":"t11-math-m1-q25","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":"Part of this question was typeset outside the text flow — a fraction, subscript or similar — and PDF extraction re-inserted it in the wrong place. The wording is reliable; the symbols may be out of order.","form_id":"cb_practice_pdf:test-11","module_number":1,"position":25,"stem":"25 + = 2x 9y 7 The given equation is one equation in a system of two linear equations. If the system of equations has at least one solution, which of the following equations could be the other equation in the system? I. 3x + 13.5y = 10.5 - = II. 3x 13.5y 10.5","stimulus":"","stimulus_html":null,"stem_html":"<p>25 + = 2x 9y 7 The given equation is one equation in a system of two linear equations. If the system of equations has at least one solution, which of the following equations could be the other equation in the system? I. 3x + 13.5y = 10.5 - = II. 3x 13.5y 10.5</p>","rationale_html":"<p>Choice C is correct. A system of two linear equations in two variables has at least one solution if the equations represent the same line or lines that intersect at 3 +13.5 =10.5 exactly one point. Statement I gives the equation x y . Multiplying 2 +9 =7 3 3 +13.5 =10.5 both sides of the given equation, x y , by 2 yields x y , so the equation in statement I is equivalent to the given equation. Therefore, the system formed by these two equations represents the same line and has infinitely many 3 -13.5 =10.5 solutions. Statement II gives the equation x y . Adding the right- and 3 +13.5 =10.5 3 -13.5 =10.5 left-hand sides of x y and x y yields 3 +13.5 +3 -13.5 =10.5+10.5 6 =21 x y x y , or x . Dividing both sides of this 21 = equation by 6 yields x 6. Therefore, the lines represented by these equations 21 = intersect at exactly one point, where x 6, and the system formed by the given equation and the equation in statement II has one solution. It follows that both the equation in statement I and the equation in statement II could be the other equation in a system of equations with at least one solution. Choice A is incorrect. Both the equation in statement I and the equation in statement II could be the other equation in this system of equations with at least one solution. Choice B is incorrect. Both the equation in statement I and the equation in statement II could be the other equation in this system of equations with at least one solution. Choice D is incorrect. Both the equation in statement I and the equation in statement II could be the other equation in this system of equations with at least one solution. 41 SAT PRACTICE TEST #11 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 1</p>","correct_answer":["C"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>I only</p>","ord":0},{"label":"B","content_html":"<p>II only</p>","ord":1},{"label":"C","content_html":"<p>I and II</p>","ord":2},{"label":"D","content_html":"<p>Neither I nor II</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}}