Linear Equations: Solutions Using
Determinants with Three Variables
Thedeterminantofa22matrixisdefinedasfollows:
Thedeterminantofa33matrixcanbedefinedasshowninthe
following.
Eachminordeterminantisobtainedbycrossingoutthefirstcolumn
andonerow.
Example1
Eva
Linear Equations: Solutions Using
Determinants with Two Variables
Asquarearrayofnumbersorvariablesenclosedbetweenvertical
linesiscalledadeterminant.Adeterminantisdifferentfromamatrix
inthatadeterminanthasanumericalvalue,whereasamatrixdoes
not.Thefollowing
Linear Equations: Solutions Using
Elimination with Three Variables
Systemsofequationswiththreevariablesareonlyslightlymore
complicatedtosolvethanthosewithtwovariables.Thetwomost
straightforwardmethodsofsolvingthesetypesofequationsareby
eliminationandbyusi
Linear Equations: Solutions Using
Matrices with Three Variables
Solvingasystemofequationsbyusingmatricesismerelyan
organizedmannerofusingtheeliminationmethod.
Example1
Solvethissystemofequationsbyusingmatrices.
Thegoalistoarriveatamatrixofthefollowingform
Linear Equations: Solutions Using
Matrices with Two Variables
Amatrix(plural,matrices)isarectangulararrayofnumbersor
variables.Amatrixcanbeusedtorepresentasystemofequationsin
standardformbywritingonlythecoefficientsofthevariablesandthe
constantsintheequat
Linear Equations: Solutions Using
Elimination with Two Variables
Tosolvesystemsusingelimination,followthisprocedure.
Arrangebothequationsinstandardform,placinglikevariables
andconstantsoneabovetheother.
Chooseavariabletoeliminate,andwithaproperchoiceof
mu
Linear Equations: Solutions Using
Graphing with Two Variables
Example1
Solvethissystemofequationsbygraphing.
Tosolveusinggraphing,graphbothequationsonthesamesetof
coordinateaxesandseewherethegraphscross.Theorderedpairat
thepointofintersectionbecomesthesol