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