{"id":1753,"date":"2015-11-12T18:30:45","date_gmt":"2015-11-12T18:30:45","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&#038;p=1753"},"modified":"2015-11-12T18:30:45","modified_gmt":"2015-11-12T18:30:45","slug":"introduction-to-systems-of-nonlinear-equations-and-inequalities-two-variables","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/chapter\/introduction-to-systems-of-nonlinear-equations-and-inequalities-two-variables\/","title":{"raw":"Introduction to Systems of Nonlinear Equations and Inequalities: Two Variables","rendered":"Introduction to Systems of Nonlinear Equations and Inequalities: Two Variables"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\nBy the end of this section, you will be able to:\n<ul><li>Solve a system of nonlinear equations using substitution.<\/li>\n\t<li>Solve a system of nonlinear equations using elimination.<\/li>\n\t<li>Graph a nonlinear inequality.<\/li>\n\t<li>Graph a system of nonlinear inequalities.<\/li>\n<\/ul><\/div>\nHalley\u2019s Comet\u00a0orbits the sun about once every 75 years. Its path can be considered to be a very elongated ellipse. Other comets follow similar paths in space. These orbital paths can be studied using systems of equations. These systems, however, are different from the ones we considered in the previous section because the equations are not linear.\n\n[caption id=\"\" align=\"aligncenter\" width=\"488\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202118\/CNX_Precalc_Figure_09_03_0012.jpg\" alt=\"A comet streaking across a starry sky.\" width=\"488\" height=\"358\" data-media-type=\"image\/jpg\"\/><b>Figure 1.<\/b> Halley\u2019s Comet (credit: \"NASA Blueshift\"\/Flickr)[\/caption]\n\nIn this section, we will consider the intersection of a parabola and a line, a circle and a line, and a circle and an ellipse. The methods for solving systems of nonlinear equations are similar to those for linear equations.","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Solve a system of nonlinear equations using substitution.<\/li>\n<li>Solve a system of nonlinear equations using elimination.<\/li>\n<li>Graph a nonlinear inequality.<\/li>\n<li>Graph a system of nonlinear inequalities.<\/li>\n<\/ul>\n<\/div>\n<p>Halley\u2019s Comet\u00a0orbits the sun about once every 75 years. Its path can be considered to be a very elongated ellipse. Other comets follow similar paths in space. These orbital paths can be studied using systems of equations. These systems, however, are different from the ones we considered in the previous section because the equations are not linear.<\/p>\n<div style=\"width: 498px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25202118\/CNX_Precalc_Figure_09_03_0012.jpg\" alt=\"A comet streaking across a starry sky.\" width=\"488\" height=\"358\" data-media-type=\"image\/jpg\" \/><\/p>\n<p class=\"wp-caption-text\"><b>Figure 1.<\/b> Halley\u2019s Comet (credit: &#8220;NASA Blueshift&#8221;\/Flickr)<\/p>\n<\/div>\n<p>In this section, we will consider the intersection of a parabola and a line, a circle and a line, and a circle and an ellipse. The methods for solving systems of nonlinear equations are similar to those for linear equations.<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1753\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Precalculus. <strong>Authored by<\/strong>: OpenStax College. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface\">http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":276,"menu_order":1,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Precalculus\",\"author\":\"OpenStax College\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1753","chapter","type-chapter","status-publish","hentry"],"part":1751,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1753","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/wp\/v2\/users\/276"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1753\/revisions"}],"predecessor-version":[{"id":2271,"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1753\/revisions\/2271"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/1751"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1753\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/wp\/v2\/media?parent=1753"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1753"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/wp\/v2\/contributor?post=1753"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/wp-json\/wp\/v2\/license?post=1753"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}