How do solve the following linear system?: # -x+5y=-13 , -4x-15y=-1 #?

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Answer 1 · 2015-11-25T01:50:26

#x=(-40)/7#
#y=(-51)/35#

Given -

#-x+5y=-13# ----------------(1)
#-4x-15y=-1# --------------(2)

Solve equation (1) for #x#

#-x=-13-5y#
#x=13+5y#

Substitute #x=13+5y# in equation (2)

#-4(13+5y)-15y=-1#

#-52-20y-15y=-1#
#-52-35y=-1#
#-35y=-1+52=51#
#-35y=51#
#y=(51)/(-35)=(-51)/35#
#y=(-51)/35#

Substitute #y=(-51)/35# in equation (1)

#-x+5(-51/35)=-13#
#-x-255/35=-13#
#-x-51/7=-13#
#-x=-13+51/7=(-91+51)/7=(-40)/7#
#x=(-40)/7#