Use Cramer's rule to solve the simultaneous equations: #4x-y+3z=11," " 2x+z =5 and -3x+2z+y=5#?

1 Answer
Nallasivam V
Aug 28, 2017

#x=4#
#z=-3#
#y=-4#

Explanation:

Given -

#4x-y+3z=11# -----------------(1)

#2x+z=5# ---------------------(2)

#-3x+2z+y=5# ---------------(3)

Take equations (1) and (2)

#4x-y+3z=11# -----------------(1)
#-3x+y+2z=5# ---------------(3) Add (1) and (3) to eliminate #y#
#x+5z=16# ---------------------(4)

Take equations (2) and (4)

#2x+z=5# ---------------------(2)
#x+5z=16# ---------------------(4) #xx 2#

#2x+z=5# ---------------------(2)
#2x+10z=32#------------------(5) -------- (2) - (5)
#-9z=27#
#z=27/(-9)=-3#

#z=-3#

Substitute #z=-3# in equation (2)

#2x+(-3)=5#
#2x-3=5#
#2x=5+3=8#
#x=8/2=4#
#x=4#

Substitute #x=4# and #z=-3) # in equation (1)

#4x-y+3z=11#
#4(4)-y+3(-3)=11#
#16-y-9=11#
#-y+7=11#
#-y=11-7=4#
#y=-4#

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