How do solve the following linear system?: #-7x + y = -19 , x - 3y = -6 #?

1 Answer
Mar 31, 2018

Answer:

Hence, the values of x and y are
#(x,y)-=(63/20,61/20)#

Explanation:

#-7x+y=-19#.........(1)

#x-3y=-6#..........(2)

Eliminating x from (2)

#x=3y-6#

Substituting for x in (1)

#-7x+y=-19#

#-7(3y-6)+y=-19#

#-7xx3y+7xx6+y=-19#

#-21y+42+y=-19#

#(-21y+y)=-19-42#

#-20y=-61#

#y=61/20#

#x=3y-6#

#x=3xx61/20-6#

#x=(3xx61)/20-(6xx20)/20#

#x=(183-120)/20#

#x=63/20#

Checking,,

#-7x+y=-19#

lhs=
#-7x+y=#
#-7xx63/20+61/20#
#=(-7xx63+61)/20#
#=(-441+61)/20#
#=-380/20#
#=-19#
=rhs

#x-3y=-6#

lhs=
#x-3y=#
#63/20-3xx61/20#

#=(63-3xx61)/20#

#(63-183)/20#

#-120/20#

#=-6#

=rhs

Hence, the values of x and y are
#(x,y)-=(63/20,61/20)#