y = 4x y = x^2 −12 (x,y) A solution to the given system of equations is, where x > 0. What is the value of x?
","rationale_html":"= = 2-12 = The correct answer is 6. It’s given that y 4x and y x . Since y 4x, substituting 4x for y in the second equation of the given system yields 4 = 2-12 x x . Subtracting 4x from both sides of this equation yields 0= 2-4 -12 0= -6 +2 x x . This equation can be rewritten as ^x h^x h. By the zero -6=0 +2=0 product property, x or x . Adding 6 to both sides of the equation -6=0 = +2=0 x yields x 6. Subtracting 2 from both sides of the equation x =- yields x 2. Therefore, solutions to the given system of equations occur when = =- x 6 and when x 2. It’s given that a solution to the given system of equations 2 is ^x,yh, where x 0. Since 6 is greater than 0, it follows that the value of x is 6.
","correct_answer":["6"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[],"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}}