What is the value of #x# in the system of equations #x-z=7, x+y=3#, and #z-y=6#?

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Answer 1 · 2017-02-07T08:21:36

#x=8#

The equations given are

#x-z=7# ...........................(1)
#x+y=3# ...........................(2) and
#z-y=6# ...........................(3)

Adding all the three, we get

#x-z+x+y+z-y=7+3+6#

or #2x=16# i.e. #x=8#

Putting this in (2), we get #8+y=3# i.e. #y=3-8=-5#

and putting #y=-5# in (3) we get

#z-(-5)=6# or #z+5=6# i.e. #z=6-5=1#

Hence solution is #x=8#, #y=-5# and #z=1#