Question

HELP ASAP!!!
Which system is inconsistent and independent

Answer 1

D

Explanation:

Just did it on edg!

Answer 2

x-y-z=2

x+y-z=3

-x+y+z=4

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 :

`2x=5 \\x=(5)/(2)`

Subtract second two :

`2y=-1\\y=-(1)/(2)`

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