{"id":242,"date":"2022-04-13T08:48:34","date_gmt":"2022-04-13T08:48:34","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=242"},"modified":"2025-04-09T10:33:14","modified_gmt":"2025-04-09T10:33:14","slug":"n-8-find-the-number-of-solutions","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/n-8-find-the-number-of-solutions\/","title":{"rendered":"N.8 Find the number of solutions"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Find the number of solutions<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\">Key Notes :<\/p>\n\n\n\n<p class=\"has-large-font-size\">If solving an equation yields a statement that is false, like 4&nbsp;=&nbsp;3, then the equation has no solution.<\/p>\n\n\n\n<p class=\"has-large-font-size\">If solving an equation yields a statement that is true for a single value for the variable, like&nbsp;<em>x<\/em>&nbsp;=&nbsp;3, then the equation has one solution.<\/p>\n\n\n\n<p class=\"has-large-font-size\">If solving an equation yields a statement that is always true, like 3&nbsp;=&nbsp;3, then the equation has infinitely many solutions.<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#abd0f1\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>How many solutions does this equation have?<\/strong><\/p>\n\n\n\n<p>2<em>n<\/em>&nbsp;\u2212 10<em>n<\/em>&nbsp;=&nbsp;\u20138<em>n<\/em><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>no solution<\/li>\n\n\n\n<li>one solution<\/li>\n\n\n\n<li>infinitely many solutions<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Solve for&nbsp;<em><em>n<\/em><\/em>.<\/p>\n\n\n\n<p>2<em>n<\/em>&nbsp;\u2212 10<em>n<\/em>&nbsp;=&nbsp;\u20138<em>n<\/em><\/p>\n\n\n\n<p>\u20138<em>n<\/em>&nbsp;=&nbsp;\u20138n         Combine like terms<\/p>\n\n\n\n<p>0&nbsp;=&nbsp;0             Add <em>8n&nbsp;<\/em>to both sides<\/p>\n\n\n\n<p><br>The statement 0 = 0 is true for every value of&nbsp;<em>n<\/em>. So, the equation is an identity and has infinitely many solutions.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#e7aac7\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>How many solutions does this equation have?<\/strong><\/p>\n\n\n\n<p>0 = 2<em>j<\/em>&nbsp;\u2212 2<em>j<\/em><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>no solution<\/li>\n\n\n\n<li>one solution<\/li>\n\n\n\n<li>infinitely many solutions<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Solve for&nbsp;<em><em>j<\/em><\/em>.<\/p>\n\n\n\n<p>0&nbsp;=&nbsp;2<em>j<\/em>&nbsp;\u2212 2<em>j<\/em><\/p>\n\n\n\n<p>0&nbsp;=&nbsp;0         Combine like terms<br><\/p>\n\n\n\n<p>The statement 0 = 0 is true for every value of&nbsp;<em>j<\/em>. So, the equation is an identity and has infinitely many solutions.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#aee395\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>How many solutions does this equation have?<\/strong><\/p>\n\n\n\n<p>3<em>q<\/em>&nbsp;= 10 + 3<em>q<\/em><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>no solution<\/li>\n\n\n\n<li>one solution<\/li>\n\n\n\n<li>infinitely many solutions<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Solve for&nbsp;<em><em>q<\/em><\/em>.<\/p>\n\n\n\n<p>3<em>q<\/em>&nbsp;=&nbsp;10 + 3<em>q<\/em><\/p>\n\n\n\n<p>0&nbsp;=&nbsp;10      Subtract 3q&nbsp;from both sides<\/p>\n\n\n\n<p>The statement 0 = 10 is false. So, the equation has no solution.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/90149\/597\/404\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-92.png\" alt=\"\" class=\"wp-image-7968\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-92.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-92-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-92-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/90148\/159\/321\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-101.png\" alt=\"\" class=\"wp-image-7969\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-101.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-101-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-101-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Find the number of solutions Key Notes : If solving an equation yields a statement that is false, like 4&nbsp;=&nbsp;3, then the equation has no solution. If solving an equation yields a statement that is true for a single value for the variable, like&nbsp;x&nbsp;=&nbsp;3, then the equation has one solution. If solving an equation yields<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/n-8-find-the-number-of-solutions\/\">Continue reading <span class=\"screen-reader-text\">&#8220;N.8 Find the number of solutions&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-242","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/242","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=242"}],"version-history":[{"count":14,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/242\/revisions"}],"predecessor-version":[{"id":16696,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/242\/revisions\/16696"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=242"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}