{"id":3197,"date":"2025-08-15T22:34:42","date_gmt":"2025-08-15T22:34:42","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=3197"},"modified":"2025-09-23T20:31:40","modified_gmt":"2025-09-23T20:31:40","slug":"solving-systems-with-cramers-rule-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/solving-systems-with-cramers-rule-apply-it\/","title":{"raw":"Solving Systems with Cramer\u2019s Rule: Apply It","rendered":"Solving Systems with Cramer\u2019s Rule: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Evaluate 2 \u00d7 2 and 3 \u00d7 3 determinants.<\/li>\r\n \t<li>Use Cramer\u2019s Rule to solve a system of equations in two variables.<\/li>\r\n \t<li>Use Cramer\u2019s Rule to solve a system of three equations in three variables.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<div>\r\n<div class=\"grid-cols-1 grid gap-2.5 [&amp;_&gt;_*]:min-w-0 !gap-3.5\">\r\n<div class=\"grid-cols-1 grid gap-2.5 [&amp;_&gt;_*]:min-w-0 !gap-3.5\">\r\n<h2 class=\"text-xl font-bold text-text-100 mt-1 -mb-0.5\">Using Cramer's Rule with Technology<\/h2>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]312639[\/ohm_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]312641[\/ohm_question]<\/section><section class=\"textbox interact\" aria-label=\"Interact\">Use the TI-84 to calculate each determinant.\r\n<ol data-start=\"1465\" data-end=\"1906\">\r\n \t<li data-start=\"237\" data-end=\"286\">\r\n<p data-start=\"240\" data-end=\"286\">Enter the coefficient matrix into matrix [A]:<\/p>\r\n\r\n<ol data-start=\"1465\" data-end=\"1906\">\r\n \t<li data-start=\"237\" data-end=\"286\">\r\n<p data-start=\"240\" data-end=\"286\">Press 2nd then x^-1 to open the MATRIX menu.<\/p>\r\n<\/li>\r\n \t<li data-start=\"237\" data-end=\"286\">\r\n<p data-start=\"240\" data-end=\"286\">Use the arrow keys to move to EDIT, select [A], set dimensions to 2 x 2, and enter the coefficients of the system.<\/p>\r\n<\/li>\r\n \t<li data-start=\"237\" data-end=\"286\">\r\n<p data-start=\"240\" data-end=\"286\">Quit to the home screen.<\/p>\r\n<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li data-start=\"237\" data-end=\"286\">Repeat steps 1\u20133 from Step 1 to create matrix [latex][D_x][\/latex] in [B] by replacing the first column of A with the constants, then compute det(B).<\/li>\r\n \t<li data-start=\"663\" data-end=\"782\">\r\n<p data-start=\"666\" data-end=\"782\">Repeat steps 1\u20133 from Step 1 to create matrix [latex][D_y][\/latex] in [C] by replacing the second column of A with the constants, then compute det(C).<\/p>\r\n<\/li>\r\n \t<li data-start=\"237\" data-end=\"286\">\r\n<p data-start=\"240\" data-end=\"286\">Find the determinant of [A]:<\/p>\r\n\r\n<ol data-start=\"1465\" data-end=\"1906\">\r\n \t<li data-start=\"237\" data-end=\"286\">\r\n<p data-start=\"240\" data-end=\"286\">Go back to MATRIX, then MATH, and select det(.<\/p>\r\n<\/li>\r\n \t<li data-start=\"237\" data-end=\"286\">\r\n<p data-start=\"240\" data-end=\"286\">Insert [A] and press ENTER to compute the determinant of A.<\/p>\r\n<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li data-start=\"783\" data-end=\"864\">\r\n<p data-start=\"786\" data-end=\"864\">On the home screen, type det(B)\/det(A) to get x, and det(C)\/det(A) to get y.<\/p>\r\n<\/li>\r\n \t<li data-start=\"865\" data-end=\"949\">\r\n<p data-start=\"868\" data-end=\"949\">If the answer shows as a decimal but you want a fraction, press MATH then Frac.<\/p>\r\n<\/li>\r\n<\/ol>\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]312643[\/ohm_question]\r\n\r\n<\/section><\/div>\r\n<\/div>\r\n<\/div>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Evaluate 2 \u00d7 2 and 3 \u00d7 3 determinants.<\/li>\n<li>Use Cramer\u2019s Rule to solve a system of equations in two variables.<\/li>\n<li>Use Cramer\u2019s Rule to solve a system of three equations in three variables.<\/li>\n<\/ul>\n<\/section>\n<div>\n<div class=\"grid-cols-1 grid gap-2.5 [&amp;_&gt;_*]:min-w-0 !gap-3.5\">\n<div class=\"grid-cols-1 grid gap-2.5 [&amp;_&gt;_*]:min-w-0 !gap-3.5\">\n<h2 class=\"text-xl font-bold text-text-100 mt-1 -mb-0.5\">Using Cramer&#8217;s Rule with Technology<\/h2>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm312639\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=312639&theme=lumen&iframe_resize_id=ohm312639&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm312641\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=312641&theme=lumen&iframe_resize_id=ohm312641&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox interact\" aria-label=\"Interact\">Use the TI-84 to calculate each determinant.<\/p>\n<ol data-start=\"1465\" data-end=\"1906\">\n<li data-start=\"237\" data-end=\"286\">\n<p data-start=\"240\" data-end=\"286\">Enter the coefficient matrix into matrix [A]:<\/p>\n<ol data-start=\"1465\" data-end=\"1906\">\n<li data-start=\"237\" data-end=\"286\">\n<p data-start=\"240\" data-end=\"286\">Press 2nd then x^-1 to open the MATRIX menu.<\/p>\n<\/li>\n<li data-start=\"237\" data-end=\"286\">\n<p data-start=\"240\" data-end=\"286\">Use the arrow keys to move to EDIT, select [A], set dimensions to 2 x 2, and enter the coefficients of the system.<\/p>\n<\/li>\n<li data-start=\"237\" data-end=\"286\">\n<p data-start=\"240\" data-end=\"286\">Quit to the home screen.<\/p>\n<\/li>\n<\/ol>\n<\/li>\n<li data-start=\"237\" data-end=\"286\">Repeat steps 1\u20133 from Step 1 to create matrix [latex][D_x][\/latex] in [B] by replacing the first column of A with the constants, then compute det(B).<\/li>\n<li data-start=\"663\" data-end=\"782\">\n<p data-start=\"666\" data-end=\"782\">Repeat steps 1\u20133 from Step 1 to create matrix [latex][D_y][\/latex] in [C] by replacing the second column of A with the constants, then compute det(C).<\/p>\n<\/li>\n<li data-start=\"237\" data-end=\"286\">\n<p data-start=\"240\" data-end=\"286\">Find the determinant of [A]:<\/p>\n<ol data-start=\"1465\" data-end=\"1906\">\n<li data-start=\"237\" data-end=\"286\">\n<p data-start=\"240\" data-end=\"286\">Go back to MATRIX, then MATH, and select det(.<\/p>\n<\/li>\n<li data-start=\"237\" data-end=\"286\">\n<p data-start=\"240\" data-end=\"286\">Insert [A] and press ENTER to compute the determinant of A.<\/p>\n<\/li>\n<\/ol>\n<\/li>\n<li data-start=\"783\" data-end=\"864\">\n<p data-start=\"786\" data-end=\"864\">On the home screen, type det(B)\/det(A) to get x, and det(C)\/det(A) to get y.<\/p>\n<\/li>\n<li data-start=\"865\" data-end=\"949\">\n<p data-start=\"868\" data-end=\"949\">If the answer shows as a decimal but you want a fraction, press MATH then Frac.<\/p>\n<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm312643\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=312643&theme=lumen&iframe_resize_id=ohm312643&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":67,"menu_order":24,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":514,"module-header":"apply_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3197"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/users\/67"}],"version-history":[{"count":5,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3197\/revisions"}],"predecessor-version":[{"id":4311,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3197\/revisions\/4311"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/514"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3197\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=3197"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=3197"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=3197"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=3197"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}