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write:30x15z=4512x=6Wecannoweasilysolveforxtogetx=12. Thecoefficientsonthesecondequationaresmallersolet’splugthisintothatequationandsolveforz. Hereisthatwork. 6123z=933z=93z=12z=4Fin

14x+5z=133!42x+15z=396x3z=95!30x15z=4512x=6Wecannoweasilysolveforxtogetx=12.Thecoefficientsonthesecondequationaresmallersolet’splugthisintothatequationandsolveforz.Hereisthatwork.6123z=933z=93z=12z=4Finally
weneedtodeterminethevalueofy.Thisisveryeasytodo.Recallinthefirststepweusedsubstitutionandinthatstepweusedthefollowingequation.y=4x+5Sinceweknowthevalueofxallweneedtodoisplugthatintothisequationandgetthevalueofy.y=412+5=3Notethatinmanycaseswhereweusedsubstitutionontheveryfirststeptheequationyou’llhaveatthisstepwillcontainbothx’sandz’sandsoyouwillneedbothvaluestogetthethirdvariable.Okay
tofinishthisexampleuphereisthesolution:x=12
y=3andz=4.Aswe’veseenwiththetwoexamplesabovethereareavarietyofpathsthatwecouldchoosetotakewhensolvingasystemofthreelinearequationswiththreevariables.Thatwillalwaysbethecase.Thereisnoonetruepathforsolvingthese.However
havingsaidthatthereisoftenapath©PaulDawkinsAlgebra–370–

 

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