How do solve the following linear system?: # 6x-4y=-1 , 3y = 15 -x #?

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Answer 1 · 2018-07-10T08:15:57

#x=57/22,y=91/22#

Writing the second equation in the form

#x=15-3y#
plugging this in the first equation

#6(15-3y)-4y=-1#
expanding we get

#90-18y-4y=-1#
substracting #90# and combining like Terms

#-22y=-91#
so
#y=91/22#

so
#x=15-3*91/22#

#x=(15*22-3*91)/22=57/22#

Answer 2 · 2018-07-10T08:21:09

#x=57/22#, #y=91/22#

The given linear equations

#6x-4y=-1\ ..........(1)#

#3y=15-x#

or

#x+3y=15\ ..........(2)#

Multiplying (2) by #6# & subtracting from (1) as follows

#6x-4y-6(x+3y)=-1-6\times 15#

#-22y=-91#

#y=91/22#

setting #y=91/22# in (2), we get

#x=15-3y#

#=15-3(91/22)#

#=57/22#