{"id":4429,"date":"2016-10-03T21:09:55","date_gmt":"2016-10-03T21:09:55","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/?post_type=chapter&p=4429"},"modified":"2017-07-27T17:01:41","modified_gmt":"2017-07-27T17:01:41","slug":"introduction-7","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/chapter\/introduction-7\/","title":{"raw":"Why It Matters: Linear Systems","rendered":"Why It Matters: Linear Systems"},"content":{"raw":"

Why learn about systems of equations and inequalities?<\/h2>\r\n[caption id=\"attachment_3935\" align=\"alignleft\" width=\"300\"]\"Alliance Alliance 2x2 Pattern RC Plane[\/caption]\r\n\r\nJoan's dad loves to build and fly model R.C. airplanes. One hot Saturday afternoon, \u00a0Joan goes with him to fly his favorite plane. \u00a0She packs them a picnic lunch and they hit the road for their favorite spot. \u00a0On the way there, Joan's dad expresses his concern that there may be a lot of turbulence because of the hot weather and the location of the field where they will fly the plane.\r\n\r\nJoan was surprised by what her dad said. \u00a0She thought turbulence only happened at high altitudes - like when you were flying in a Jet. \u00a0Later, after she and her dad got home from flying his RC plane, Joan decided to Google turbulence. \u00a0She was surprised to find that turbulence can happen on scales as small as gas or water passing through pipes.\r\n\r\nShe also learned that despite it's occurrence in most fluid flows, such as wind, rivers, oceans, and fluids moving through pipes, scientists and mathematicians have yet to find a reliable way to model or describe it's behavior with mathematics or physics. \u00a0Joan was shocked - she thought math and science had answers for everything! She read further and found that the mathematical equations that are typically used to model fluid flows have\u00a0not yet been proven to have solutions\u00a0that always exist. Joan further found that the equations are called the Navier-Stokes equations after\u00a0Claude-Louis Navier and\u00a0George Gabriel Stokes. The Navier-Stokes equations are a system of three equations that contain many variables used to describe features of the fluid\u00a0like temperature, speed, and density.\r\n\r\nJoan found that physicists and mathematicians use the Navier\u2013Stokes equations to\u00a0\u00a0model the weather, ocean currents, waterflow in a pipe and air flow around a wing. Engineers and scientists use them to design aircraft and cars, study blood flow, design power stations, and\u00a0even understand how pollution spreads.\r\n\r\nThe following week, in her algebra class, Joan learned about systems of linear equations, and how to graph them and find solutions for them. \u00a0Even though her classmates were surprised to find that some systems do not have solutions, Joan already knew about a famous system of equations that do not have any known solutions.\r\n\r\nHer teacher was very impressed when she shared what she had learned by spending an afternoon with her father flying RC airplanes.\r\n\r\nIn this module, we will learn how to graph systems of equations in two and three dimensions, and find whether solutions exist. We will also see how systems of equations can be used to solve problems where we have two or three unknown variables.","rendered":"

Why learn about systems of equations and inequalities?<\/h2>\n
\"Alliance<\/p>\n

Alliance 2×2 Pattern RC Plane<\/p>\n<\/div>\n

Joan’s dad loves to build and fly model R.C. airplanes. One hot Saturday afternoon, \u00a0Joan goes with him to fly his favorite plane. \u00a0She packs them a picnic lunch and they hit the road for their favorite spot. \u00a0On the way there, Joan’s dad expresses his concern that there may be a lot of turbulence because of the hot weather and the location of the field where they will fly the plane.<\/p>\n

Joan was surprised by what her dad said. \u00a0She thought turbulence only happened at high altitudes – like when you were flying in a Jet. \u00a0Later, after she and her dad got home from flying his RC plane, Joan decided to Google turbulence. \u00a0She was surprised to find that turbulence can happen on scales as small as gas or water passing through pipes.<\/p>\n

She also learned that despite it’s occurrence in most fluid flows, such as wind, rivers, oceans, and fluids moving through pipes, scientists and mathematicians have yet to find a reliable way to model or describe it’s behavior with mathematics or physics. \u00a0Joan was shocked – she thought math and science had answers for everything! She read further and found that the mathematical equations that are typically used to model fluid flows have\u00a0not yet been proven to have solutions\u00a0that always exist. Joan further found that the equations are called the Navier-Stokes equations after\u00a0Claude-Louis Navier and\u00a0George Gabriel Stokes. The Navier-Stokes equations are a system of three equations that contain many variables used to describe features of the fluid\u00a0like temperature, speed, and density.<\/p>\n

Joan found that physicists and mathematicians use the Navier\u2013Stokes equations to\u00a0\u00a0model the weather, ocean currents, waterflow in a pipe and air flow around a wing. Engineers and scientists use them to design aircraft and cars, study blood flow, design power stations, and\u00a0even understand how pollution spreads.<\/p>\n

The following week, in her algebra class, Joan learned about systems of linear equations, and how to graph them and find solutions for them. \u00a0Even though her classmates were surprised to find that some systems do not have solutions, Joan already knew about a famous system of equations that do not have any known solutions.<\/p>\n

Her teacher was very impressed when she shared what she had learned by spending an afternoon with her father flying RC airplanes.<\/p>\n

In this module, we will learn how to graph systems of equations in two and three dimensions, and find whether solutions exist. We will also see how systems of equations can be used to solve problems where we have two or three unknown variables.<\/p>\n","protected":false},"author":21,"menu_order":1,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4429","chapter","type-chapter","status-publish","hentry"],"part":2069,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/4429","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/4429\/revisions"}],"predecessor-version":[{"id":4545,"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/4429\/revisions\/4545"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/pressbooks\/v2\/parts\/2069"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/4429\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/wp\/v2\/media?parent=4429"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=4429"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/wp\/v2\/contributor?post=4429"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/wp\/v2\/license?post=4429"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}