最新Solving Systems Using Elimination - …教学讲义PPT.ppt

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1、SolvingSystemsUsingElimination-…EliminationWhenneitherequationisintheslope-interceptform(y=),youcansolvethesystemusingelimination.Youcanaddequationstoeliminateavariable.Lookforliketermsthatareoppositesofeachother(willaddtozero).Example15x–6y=-323x+6y=48Makesureliketermsarelinedupwitheachothe

2、r.Lookforliketermsthatareopposites(inthiscasethe–6yand+6yareopposites).Addalltheliketerms(5x+3x=8x)(-6y+6y=0)(-32+48=16)Example2Replacexwith17inthefirstequationtofindy.17–y=12Subtract17frombothsides.-y=-5Dividebothsidesby–1.y=5Replacexwith17andywith5inthesecondequationtocheck.17+5=22Thatistr

3、ue,sothesolutionis(17,5)NotAlwaysSoEasySometimestherearenotliketermsthatwilladdtozero(eliminate).Youcanmultiplyordivideallthetermsbyanynumber(exceptzero)tomakeopposites.Example33x+4y=-105x–2y=18Therearenooppositeliketerms.However,ifImultiplythesecondequationby2,they’swillbeopposites.(Thefirs

4、tequationwillstaythesame.)3x+4y=-1010x–4y=36Example3Nowaddtheliketerms.13x=26Solve.x=2Replacexinthefirstequationwith2tofindy.3(2)+4y=-106+4y=-10Subtract6frombothsides.Example34y=-16Dividebothsidesby4y=-4Checkbyreplacingxwith2andywith–4inthesecondequation.5(2)–2(-4)=1810+8=18.Thisistrue.Theso

5、lutionis(2,-4)Example47x–12y=-225x–8y=-14Ichoosetogetridofthex’s.SoIwillmultiplythetopequationby5andthebottomequationby-735x–60y=-110-35x+56y=98Nowaddtheequations.Example4-4y=-12y=3Thatisthesecondmemberoftheorderedpair.Nowfindxbyreplacingyinoneoftheequationswith3andsolveforx.7x–12(3)=-227x–3

6、6=-227x=14x=2(2,3)Trythese…2x+7y=315x–7y=-45x–6y=26x+6y=122x+5y=34x+2y=14x+6y=20x+2y=12(-2,5)(2,0)(2,6)(8,2)第二章合同的分类第一节双务合同与单务合同一、划分标准以给付是否由双方当事人互负为标准，合同分为双务合同和单务合同。二、双务合同与单务合同（一）双务合同是双方当事人互负对待给付义务的合同，即一方当事人之所以负给付义务，在于取得对待给付。如：买卖、租赁、承揽合同。（二）单务合同是仅有一方当事人负给付义务的合同。如：赠与、借用合同。三、区分双务合同与单务合同的法律意义（一

7、）双务合同适用履行抗辩权，单务合同不适用（二）双务合同因不可归责于双方当事人的原因不能履行时，发生风险负担问题。在单务合同中，因不可归责于双方当事人的原因不能履行时，风险一律由债务人负担。（三）在双务合同中，当事人一方违约时，另一方若已履行合同，则可以请求强制违约方实际履行或者承担其他违约责任，条件具备时可以解除合同；解除合同并溯及既往时，另一方有权请求违约方返还受领的给付。单务合同一般不适用解除制度。一、划分标准以当事人取得权益是否须付相应代价为标准，合同分为有偿合同与无偿合同。第二节有偿