HELP ASAP!!!Which system is inconsistent and independent

Accepted Solution

Answer:x-y-z=2x+y-z=3-x+y+z=4Step-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=2Now, add second two: (2+3)2x=4 ; x=2When 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______________________________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._________________________________Now, let  check system 3: Divide first eq. with 2 : x+y+z=2                                        -x-y-z=-2                                         x+y+z=2This system has infinite solution. When we add first two eq we got 0=0, so the same with second two._________________________Now, let check system 4:Subtract first 2 eq:-2y=5Subtract second 2:2x-2z=-1So we cannot find solution. And our answer is d