How do you solve the system in equations #0.6x + 0.1y = 2.1# and #- 2.6x - 1.3y = - 1.3#?

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Answer 1 · 2017-07-04T14:15:01

#x=5# and #y=-9#

The equations are

#0.6x+0.1y=2.1# .....................(1)

#-2.6x-1.3y=-1.3# .....................(2)

Multiplying (1) by #13# (note that this will make #+0.1y->+1.3y# and then adding to second equation eliminates #y# as it has #-1.3y#) and we get

#7.8x+1.3y=27.3# .....................(3)

Adding (2) and (3), we get

#7.8x-2.6x=27.3-1.3#

or #5.2x=26#

or #x=26/5.2=26/(52/10)=26xx10/52=cancel26^1xx10/(cancel52^2)=10/2=5#

and putting this in (1), we get

#0.6xx5+0.1y=2.1#

or #3+0.1y=2.1#

or #0.1y=2.1-3=-0.9#

Hence #y=-0.9/0.1=-9#

i.e. #x=5# and #y=-9#