{"id":1321,"date":"2013-07-31T04:20:01","date_gmt":"2013-07-31T04:20:01","guid":{"rendered":"?page_id=1321"},"modified":"2013-07-31T04:20:01","modified_gmt":"2013-07-31T04:20:01","slug":"page-378","status":"publish","type":"page","link":"https:\/\/www.collegeprepalgebra.com\/cpa\/content\/math-help\/chapter-8\/section-1\/page-378\/","title":{"rendered":"Page 378"},"content":{"rendered":"
\n

Math Help for Section 8.1, Page 378<\/h2>\n<\/h2>\n

\nSystems
\nof Linear Equations
\n<\/span>
\nUntil this chapter, most problems have involved just one equation in
\neither one or
\ntwo variables. However, many problems in science, business, health
\nservices, and
\ngovernment involve two or more equations in two or more variables. The
\nfinance problem described on page 354 is one example. <\/p>\n

Example
\n1: Tip<\/span>
\nChecking a solution of a system of equations works the same way as
\nchecking a solution of a single equation (introduced in the Math Help<\/a>
\nfor
\nsection 2.4, page 86). However, you have to substitute more than one
\nvariable into the equations and there is more than one equation to
\ncheck. When you substitute coordinates into two equations and the
\nsubstitution results in a true statement in both<\/span> equations,
\nthen the coordinate point is a solution of the system of equations. When
\nthe substitution results in
\na false statement in one<\/span>
\nor both<\/span>
\nequations, then the coordinate point is not a solution. For instance,
\ncheck whether $(-2,5)$ is a solution of the system of
\nequations in Example 1.<\/p>\n

\nIn the first equation, $3x+2y=4$, substitute $-2$ for x<\/span> and 5 for y<\/span>.\n<\/p>\n

  
\n $3({\\color{red}-2})+2({\\color{red}5})\\overset{?}{=}4\\quad\\longrightarrow\\quad
\n-6+10=4\\quad\\quad\\eqalign{&\\small\\color{red}\\text{Solution checks}
\n\\cr &\\small\\color{red}\\text{in 1st equation.}}$<\/p>\n

In the second equation, $-x+3y=-5$, substitute $-2$ for x<\/span> and 5 for y<\/span>.\n<\/p>\n

  
\n $-({\\color{red}-2})+3({\\color{red}5})\\overset{?}{=}-5\\quad\\longrightarrow\\quad
\n-2+15\\ne
\n-5\\quad\\quad\\eqalign{&\\small\\color{red}\\text{Solution does not}
\n\\cr &\\small\\color{red}\\text{check in 2nd equation.}}$<\/p>\n

Because the solution $(-2,5)$ does not check in both<\/span>
\nequations, you can conclude that it is not a solution of the original
\nsystem of equations. Also, you can see that $(-2,5)$ is not the point of intersection in
\nthe graph.\n<\/p>\n<\/div>\n


\n
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Math Help for Section 8.1, Page 378 Systems of Linear Equations Until this chapter, most problems have involved just one equation in either one or two variables. However, many problems in science, business, health services, and government involve two or … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":1319,"menu_order":1890,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-1321","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.collegeprepalgebra.com\/cpa\/wp-json\/wp\/v2\/pages\/1321","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.collegeprepalgebra.com\/cpa\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.collegeprepalgebra.com\/cpa\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.collegeprepalgebra.com\/cpa\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.collegeprepalgebra.com\/cpa\/wp-json\/wp\/v2\/comments?post=1321"}],"version-history":[{"count":0,"href":"https:\/\/www.collegeprepalgebra.com\/cpa\/wp-json\/wp\/v2\/pages\/1321\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/www.collegeprepalgebra.com\/cpa\/wp-json\/wp\/v2\/pages\/1319"}],"wp:attachment":[{"href":"https:\/\/www.collegeprepalgebra.com\/cpa\/wp-json\/wp\/v2\/media?parent=1321"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}