{"id":42295,"date":"2025-06-28T18:31:26","date_gmt":"2025-06-28T18:31:26","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=42295"},"modified":"2025-06-28T18:31:27","modified_gmt":"2025-06-28T18:31:27","slug":"which-ordered-pair-makes-both-inequalities-true-2","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/which-ordered-pair-makes-both-inequalities-true-2\/","title":{"rendered":"Which ordered pair makes both inequalities true"},"content":{"rendered":"\n<p><br>Which ordered pair makes both inequalities true? y &lt; 3x &#8211; 1 y \\geq -x + 4 (4,0) (1,2) (0,4) (2,1) Mark this and return<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"828\" height=\"828\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-465.png\" alt=\"\" class=\"wp-image-42296\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-465.png 828w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-465-300x300.png 300w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-465-150x150.png 150w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-465-768x768.png 768w\" sizes=\"auto, (max-width: 828px) 100vw, 828px\" \/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To determine which ordered pair makes both inequalities true, we need to test each option by substituting its x and y values into both of the given inequalities. The two inequalities are:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>y &lt; 3x &#8211; 1<\/li>\n\n\n\n<li>y \u2265 -x + 4<\/li>\n<\/ol>\n\n\n\n<p>A point is a solution to the system only if its coordinates satisfy both inequalities. Let&#8217;s check each ordered pair.<\/p>\n\n\n\n<p><strong>Option 1: (4, 0)<\/strong><br>First, we substitute x = 4 and y = 0 into the first inequality:<br>0 &lt; 3(4) &#8211; 1<br>0 &lt; 12 &#8211; 1<br>0 &lt; 11<br>This statement is true.<br>Next, we substitute x = 4 and y = 0 into the second inequality:<br>0 \u2265 -(4) + 4<br>0 \u2265 -4 + 4<br>0 \u2265 0<br>This statement is also true because the &#8220;or equal to&#8221; condition is met. Since (4, 0) satisfies both inequalities, it is a correct solution.<\/p>\n\n\n\n<p><strong>Option 2: (1, 2)<\/strong><br>Substitute x = 1 and y = 2 into the first inequality:<br>2 &lt; 3(1) &#8211; 1<br>2 &lt; 3 &#8211; 1<br>2 &lt; 2<br>This statement is false because 2 is not strictly less than 2. Therefore, (1, 2) is not a solution.<\/p>\n\n\n\n<p><strong>Option 3: (0, 4)<\/strong><br>Substitute x = 0 and y = 4 into the first inequality:<br>4 &lt; 3(0) &#8211; 1<br>4 &lt; 0 &#8211; 1<br>4 &lt; -1<br>This statement is false. Therefore, (0, 4) is not a solution.<\/p>\n\n\n\n<p><strong>Option 4: (2, 1)<\/strong><br>Substitute x = 2 and y = 1 into the second inequality (we can start with either):<br>1 \u2265 -(2) + 4<br>1 \u2265 -2 + 4<br>1 \u2265 2<br>This statement is false. Therefore, (2, 1) is not a solution.<\/p>\n\n\n\n<p>After testing all the options, the only ordered pair that makes both inequalities true is (4, 0). This point is located in the solution region of the graphed system.<\/p>\n\n\n\n<p>The correct answer is&nbsp;<strong>(4, 0)<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-291.jpeg\" alt=\"\" class=\"wp-image-42297\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-291.jpeg 1024w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-291-300x300.jpeg 300w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-291-150x150.jpeg 150w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-291-768x768.jpeg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Which ordered pair makes both inequalities true? y &lt; 3x &#8211; 1 y \\geq -x + 4 (4,0) (1,2) (0,4) (2,1) Mark this and return The Correct Answer and Explanation is: To determine which ordered pair makes both inequalities true, we need to test each option by substituting its x and y values into both [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-42295","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42295","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=42295"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42295\/revisions"}],"predecessor-version":[{"id":42298,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42295\/revisions\/42298"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=42295"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=42295"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=42295"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}