{"id":18416,"date":"2026-05-03T04:30:53","date_gmt":"2026-05-02T22:30:53","guid":{"rendered":"https:\/\/mcqacademy.com\/en\/mcq\/ordered-pair-system-from-sum-product-6\/"},"modified":"2026-05-03T04:30:53","modified_gmt":"2026-05-02T22:30:53","slug":"ordered-pair-system-from-sum-product-6","status":"publish","type":"mcq","link":"https:\/\/mcqacademy.com\/en\/mcq\/ordered-pair-system-from-sum-product-6\/","title":{"rendered":"Ordered Pair System From Sum Product 6"},"content":{"rendered":"<p>Find all ordered pairs (x, y) satisfying x + y = -7 and xy = 10.<\/p>\n\n<ul class=\"quiz-options wp-block-list\">\n<li>(-1, -6)<\/li>\n<li>(-2, -5)<\/li>\n<li>(-7, 10)<\/li>\n<li>(10, -7)<\/li>\n<li>(-5, -2)<\/li>\n<\/ul>\n","protected":false},"author":39,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","topic":[2705],"subject":[1425],"education_level":[1896],"class_list":["post-18416","mcq","type-mcq","status-publish","hentry","topic-algebra","subject-mathematics","education_level-hsc"],"mcq_note":"Here x and y are two numbers whose sum is -7 and product is 10. A useful HSC-level trick is to think of them as roots of the quadratic equation t\u00b2 - (-7)t + (10) = 0. After factoring or solving that quadratic, we get the two possible numbers. Since the question asks for ordered pairs, the order matters: if the two numbers are different, both (first, second) and (second, first) are valid. Checking the selected pair(s), each one has sum -7 and product 10. Therefore the correct answer choices are (-2, -5), (-5, -2).","mcq_options":[{"right":"no","answer":"(-1, -6)"},{"right":"yes","answer":"(-2, -5)"},{"right":"no","answer":"(-7, 10)"},{"right":"no","answer":"(10, -7)"},{"right":"yes","answer":"(-5, -2)"}],"multi_answers":"yes","subject_terms":[{"id":1425,"title":"Mathematics","slug":"mathematics"}],"topic_terms":[{"id":2705,"title":"Algebra","slug":"algebra"}],"_links":{"self":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/mcq\/18416","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/mcq"}],"about":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/types\/mcq"}],"author":[{"embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/users\/39"}],"replies":[{"embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/comments?post=18416"}],"wp:attachment":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/media?parent=18416"}],"wp:term":[{"taxonomy":"topic","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/topic?post=18416"},{"taxonomy":"subject","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/subject?post=18416"},{"taxonomy":"education_level","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/education_level?post=18416"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}