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write:So whatdoesthismeanforus?Welliftwolineshavethesameslopeandthesamey-interceptthenthegraphsofthetwolinesarethesamegraph. Inotherwords thegraphsofthesetwolinesarethesamegraph. Inthese

thisisclearlynotwhatwewereexpectingforananswerhereandsoweneedtodeterminejustwhatisgoingon.We’llleaveittoyoutoverifythis
butifyoufindtheslopeandy-interceptsforthesetwolinesyouwillfindthatbothlineshaveexactlythesameslopeandbothlineshaveexactlythesamey-intercept.So
whatdoesthismeanforus?Welliftwolineshavethesameslopeandthesamey-interceptthenthegraphsofthetwolinesarethesamegraph.Inotherwords
thegraphsofthesetwolinesarethesamegraph.Inthesecasesanysetofpointsthatsatisfiesoneoftheequationswillalsosatisfytheotherequation.Also
recallthatthegraphofanequationisnothingmorethanthesetofallpointsthatsatisfiestheequation.Inotherwords
thereisaninfinitesetofpointsthatwillsatisfythissetofequations.Inthesecaseswedowanttowritedownsomethingforasolution.So
whatwe’lldoissolveoneoftheequationsforoneofthevariables(itdoesn’tmatterwhichyouchoose).We’llsolvethefirstfory.2x+5y=15y=2x1y=25×15©PaulDawkinsAlgebra–365–

 

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