How do you solve the system #x+y-z=0-1#, #4x-3y+2z=16#, #2x-2y-3z=5#?

1 Answer
Dec 28, 2015

#x+y-z=0-1##impliesx+y-z=-1...............(i)#
#4x-3y+2x=16............(ii)#
#2x-2y-3z=5.................(iii)#

Multiply #(i)# by -4 and add in #(ii)#
#implies -4x-4y+4z=4#
#+4x-3y+2z=16#
By addition we have
#-7y+6z=20##................(iv)#

Again multiply #(i)# by -2 and add in #(iii)#
#implies -2x-2y+2z=2#
#+2x-2y-3z=5#

By addition we have
#-4y-z=7............(v)#

Mutiply #(v)# by #6# and add in #(iv)#
#implies -24y-6z=42#
#-7y+6z=20#

By addition we have
#-31y=62#
#implies y=-2#

put #y=-2# in #(v)#
#implies -4(-2)-z=7#
#implies 8-z=7#
#implies z=1#

Now put #y=-2# and #z=1# in #(i)#
#implies x-2-1=-1#
#implies x-3=-1#
#implies x=2#