1.4SolvingLinearSystemsDoNow:Solvethesystemofequations2" − 3% = −24" + % = 24Youhavesolvedsystemsoflinearequationswithsubstitution,elimination,andgraphing.Letustakealookinanewdimension!(X,Y,Z)Example1:SolvingaThree-VariableSystemSolvethesystem:

4" + 2% + 3) = 122" − 3% + 5) = −76" − % + 4) = −3

Example2:SolvingaThree-VariableSystemSolvethesystem:

" + % + ) = 25" + 5% + 5) = 34" + % − 3) = −6

Example3:SolvingaThree-VariableSystemSolvethesystem

" − % + ) = −3" − % − ) = −3

5" − 5% + ) = −15

Tryonyourown:

Example4:ModelingwithMathematicsPNCBankArtCenterisanamphitheaterthatchanges$75foreachseatinSectionA,$55foreachseatinSectionB,and$30foreachlawnseat.TherearethreetimesasmanyseatsinSectionBasinSectionA.Therevenuefromsellingall23,000seatsis$870,000.Howmanyseatsareineachsectionoftheamphitheater?Homework:3,5,7,12,14,18,34,41,43*