(3; - 1) x + z = 4+y x + (y - 3) - 5 = 0

To solve the system of equations:

1. From the first equation, we have: x + z = 4 + y -- (Equation 1)

2. From the second equation, we have: x + (y - 3) - 5 = 0 -- (Equation 2)

To determine the values of x, y, and z, we can use substitution or elimination method. Let's use elimination method in this case:

To eliminate x, we can subtract Equation 2 from Equation 1.

Subtracting Equation 2 from Equation 1, we get: (x + z) - (x + (y - 3) - 5) = (4 + y) - (0)

Simplifying the left side, we have: z + y - 3 + 5 = 4 + y

Simplifying the right side, we have: z + y + 2 = 4 + y

Rearranging the equation, we get: z = 4 + y - y - 2

Simplifying further, we have: z = 4 - 2

Therefore, z = 2.

We now have one of the variables as z.

To determine the value of y, we can substitute the value of z back into either Equation 1 or Equation 2.

Substituting z = 2 into Equation 1, we get: x + 2 = 4 + y

Subtracting 2 from both sides, we have: x = 4 + y - 2

Simplifying further, we have: x = 2 + y

We now have the value of x in terms of y.

To determine the value of y, we need one additional equation. If there are no additional equations provided, the solution for y may be infinite.

Without further information, we cannot determine the values of x, y, and z.