Answer:
x-y-z=2
x+y-z=3
-x+y+z=4
Step-by-step explanation:
If system has no solution it is inconsistent.
When we look first system we can find solution.
System 1:x-y+z=2 (1)
x-y-z=2 (2)
x+y+z=2 (3)
Subtract first two eq. of system 1, and we got :
2z=4, so z=2
Now, add second two: (2+3)
2x=4 ; x=2
When we have x=2, z=2 we can find y from any of those equation.
(1) 2-y+2=2
-y=-2 then y=2
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Now, let check system 2:
When we add first two equation of system we got :
[tex]2x=5 \\x=\frac{5}{2}[/tex]
Subtract second two :
[tex]2y=-1\\y=-\frac{1}{2}[/tex]
When we have x and y it is easy to find z.
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Now, let check system 3:
Divide first eq. with 2 : x+y+z=2
-x-y-z=-2
x+y+z=2
This system has infinite solution. When we add first two eq we got 0=0, so the same with second two.
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Now, let check system 4:
Subtract first 2 eq:
-2y=5
Subtract second 2:
2x-2z=-1
So we cannot find solution.
And our answer is d
