How do solve the following linear system?: # 2x-y=4 , 3x – 4y = 7 #?

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Answer 1 · 2017-02-03T05:25:53

#x=9/5#
#y=-2/5#

Given -

#2x-y=4#------------------(1)
#3x-4y=7#-----------------(2)

Solve equation (1) for #y#

#2x-y=4#
#-y=4-2x#
#y=-4+2x#

Substitute #y=-4+2x# in equation (2)

#3x-4y=7#
#3x-4(-4+2x)=7#
#3x+16-8x=7#
#-5x=7-16=-9#
#x=(-9)/(-5)=9/5#
#x=9/5#

Substitute #x=9/5# in eqation (1)

#2x-y=4#
#2(9/5)-y=4#
#18/5-y=4#
#-y=4-18/5#
#-y=(20-18)/5=2/5#
#y=-2/5#