Solve the system of equations. If the system is dependent, express solutions in terms of the parameter z.

x-y+z = - 1

x+y+z=5

x+y-z=-3

Express x from first equation:

x = y - z - 1

Replace x with found value in second equation and solve it:

y - z - 1 + y + z = 5

2y - 1 = 5

2y = 6

y = 3

Replace x with found value in third equation:

y - z - 1 + y - z = - 3

Replace y with found value in this equation and solve it:

3 - z - 1 + 3 - z = - 3

-2z = - 3 - 3 + 1 - 3

-2z = - 8

2z = 8

z = 4

Find x by replacing y and z in first equation and solving it:

x = y - z - 1

x = 3 - 4 - 1 = - 2

So x = - 2, y = 3, z = 4