{"id":197,"date":"2020-04-18T14:16:38","date_gmt":"2020-04-18T18:16:38","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/?post_type=chapter&p=197"},"modified":"2021-06-24T16:27:28","modified_gmt":"2021-06-24T20:27:28","slug":"equations-and-functions","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/chapter\/equations-and-functions\/","title":{"raw":"2.4 Equations and Functions","rendered":"2.4 Equations and Functions"},"content":{"raw":"
\r\n

Key Takeaways<\/p>\r\n\r\n<\/header>\r\n

In linear equations it is always possible to solve for any variable shown in the equation<\/em><\/div>\r\n<\/div>\r\n \r\n\r\nAn equation always shows a relationship between variables, but the relationship is not necessarily to be viewed as a function with independent and dependent variables. For example, in the equation [latex]4p+3q=7[\/latex], there is no requirement that one variable be independent and the other dependent.\r\n\r\nIn linear equations it is always possible to solve for any variable shown in the equation -that is, to rewrite the equation with that variable by itself on one side of the equation. If this is done, it is a convention to write the variable on the left-hand side of the equation and treat it as the dependent variable. Thus, in the example above, you could solve for p<\/em> as follows:\r\n

[latex]p = \\frac{7}{4}-\\frac{3q}{4}[\/latex]<\/p>\r\nand treat p<\/em> as a function of q<\/em>. Similarly you could solve for q as follows:\r\n

[latex]q = \\frac{7}{3}-\\frac{4p}{3}[\/latex]<\/p>\r\nand treat \u00a0as a function of p<\/em>.\r\n\r\n \r\n

Your Own Notes<\/h2>\r\n
    \r\n \t
  • Are there any notes you want to take from this section? Is there anything you'd like to copy and paste below?<\/li>\r\n \t
  • These notes are for you only (they will not be stored anywhere)<\/li>\r\n \t
  • Make sure to download them at the end to use as a reference<\/li>\r\n<\/ul>\r\n[h5p id=\"1\"]","rendered":"
    \n
    \n

    Key Takeaways<\/p>\n<\/header>\n

    In linear equations it is always possible to solve for any variable shown in the equation<\/em><\/div>\n<\/div>\n

     <\/p>\n

    An equation always shows a relationship between variables, but the relationship is not necessarily to be viewed as a function with independent and dependent variables. For example, in the equation [latex]4p+3q=7[\/latex], there is no requirement that one variable be independent and the other dependent.<\/p>\n

    In linear equations it is always possible to solve for any variable shown in the equation -that is, to rewrite the equation with that variable by itself on one side of the equation. If this is done, it is a convention to write the variable on the left-hand side of the equation and treat it as the dependent variable. Thus, in the example above, you could solve for p<\/em> as follows:<\/p>\n

    [latex]p = \\frac{7}{4}-\\frac{3q}{4}[\/latex]<\/p>\n

    and treat p<\/em> as a function of q<\/em>. Similarly you could solve for q as follows:<\/p>\n

    [latex]q = \\frac{7}{3}-\\frac{4p}{3}[\/latex]<\/p>\n

    and treat \u00a0as a function of p<\/em>.<\/p>\n

     <\/p>\n

    Your Own Notes<\/h2>\n
      \n
    • Are there any notes you want to take from this section? Is there anything you’d like to copy and paste below?<\/li>\n
    • These notes are for you only (they will not be stored anywhere)<\/li>\n
    • Make sure to download them at the end to use as a reference<\/li>\n<\/ul>\n
      \n