Answer: The correct option is option third, i.e., consistent and independent.
Explanation:
The system of equation have three equation,
[tex]x=5[/tex] ..... (1)
[tex]y=6[/tex] ..... (2)
[tex]-x-y+z=0[/tex] .... (3)
Put the value of x and y from equation (1) and (2) in equation (3).
[tex]-5-6+z=0[/tex]
[tex]-11+z=0[/tex]
[tex]z=11[/tex]
The given system of equation have a unique solution (5,6,11).
The system of equation is inconsistent if there is no solution and consistent if there exist at least one solution. If the solution is unique the it is independent and if there are more than one solutions then it is dependent.
Since in above calculation we find the values of (x,y,z) and we get a unique value for each variable, it means the solution is unique and the system of linear equation is consistent and independent.
Therefore the option third is correct.
