1-1 Introduction to Linear Equations

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1、x1-1IntroductiontoLinearEquationsx1-1IntroductiontoLinearEquationstkzg@jnu.edu.cntkzg@jnu.edu.cn1/33x1-1IntroductiontoLinearEquationsContentstkzg@jnu.edu.cn2/33x1-1IntroductiontoLinearEquationsContentsMotivationExamplestkzg@jnu.edu.cn2/33x1-1IntroductiontoLinearEquationsContentsMotivatio

2、nExamplesSystemsofLinearEquationstkzg@jnu.edu.cn2/33x1-1IntroductiontoLinearEquationsContentsMotivationExamplesSystemsofLinearEquationsLinearSystemsinTwovariablestkzg@jnu.edu.cn2/33x1-1IntroductiontoLinearEquationsContentsMotivationExamplesSystemsofLinearEquationsLinearSystemsinTwovariab

3、lesIGraphicMethodtkzg@jnu.edu.cn2/33x1-1IntroductiontoLinearEquationsContentsMotivationExamplesSystemsofLinearEquationsLinearSystemsinTwovariablesIGraphicMethodIEliminationMethodtkzg@jnu.edu.cn2/33x1-1IntroductiontoLinearEquationsMotivationExamplesExample(/êÓ<)8kWêÓ<§þkn›ÊÞ§ekÊ›ov§¯WêˆAÛ

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8、5šfŽ²6Solution:Letxdenotethenumberofhens,andydenotethenumberofrabbits.Thenx+y=35;2x+4y=94:tkzg@jnu.edu.cn3/33x1-1IntroductiontoLinearEquationsMotivationExamplesExampl

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13、5ܣ6Solution:Letx1,x2andx3denotethenumberofthecocks,hensandchickens,respectively.Thenx1+x2+x3=100;

14、15x1+3x2+x3=100:3tkzg@jnu.edu.cn4/33x1-1IntroductiontoLinearEquationsMotivationExamplesExample(LeontifExchangeModel)Assumethataneconomyconsistsofthecoal,electric,andsteelsectors.TheoutputofeachsectorisdistributedamongvarioussectorsasinthefollowingtablePurchasedbyCoalElectricSteelCoal00.4

15、0.6Electric0.60.10.2Steel0.40.50.2tkzg@jnu.edu.cn5/33x1-1IntroductiontoLinearEquationsMotivationExamplesExample(LeontifExchangeModel)Assumethataneconomyconsistsofthecoal,electric,andsteelsectors.TheoutputofeachsectorisdistributedamongvarioussectorsasinthefollowingtablePur