Question #9ab83

1 Answer
Mar 23, 2017

Answer:

#x=4,y=0,z=-3#

Explanation:

Given three equation and three unknown
#x+y-z=7# .......(1)
#-2x+2y-z=-5# .......(2)
#3x-3y+2z=6# ......(3)

Step 1. Eliminate one unknown from first two equations. Let us take #z#

Subtracting (2) from (1) we get
#(x+y-z)-(-2x+2y-z)=7-(-5)#
#=>x+y-z+2x-2y+z=7+5#
#=>3x-y=12# ......(4)

Step 2. Eliminate same unknown from next two equations. (one can choose last two as well).

Multiplying (2) with #2# and adding (3)
#2xx(-2x+2y-z)+(3x-3y+2z)=2xx(-5)+6#
#=>-4x+4y-2z+3x-3y+2z=-10+6#
#=>-x+y=-4# .....(5)

We now have two equations (4) and (5) with two unknowns.
Step 3. Eliminate one unknown from these two equations.

We see that if we add these two we eliminate #y#. We get
#3x-y+(-x+y)=12+(-4)#
#=>3x-y-x+y=12-4#
#=>2x=8#
#=>x=8/2#
#=>x=4#

Step 4. Insert this value of #x# in either (4) or (5) to obtain #y#. Let us choose (5)

#-4+y=-4#
#y=-4+4#
#y=0#

Step 5. Insert these values of #x and y# in any of (1), (2) or (3) to obtain #z#. Let us choose (1)

#4+0-z=7#
#=>z=4-7#
#=>z=-3#