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(x,y,z) = (2,-2,1)

Step-by-step explanation:

Three equations with three variables are given. Take two equations at a time to eliminate one variable.

                      x + y - z = -1                       (1)

                   4x -3y + 2z = 16                   (2)

                    2x - 2y - 3z = 5                   (3)

Solve (1) and (3) to eliminate z.

To do that multiply (1) by 2 and add (1) and (2). We get:

                        4x - 5z = 3                       (4)

Now, solve (2) and (3) and subtract them. We get:

                        2x + 13z = 17                    (5)

Solve (4) and (5). Multiply (5) by 2 and subtract. We get:

                                        z  = 1

Substituting z = 1, in (4) we get:  x = 2.

Now to find y, substitute values of x and y in (1).

⇒ x + y - z = -1 ⇒ 2 + y - 1 = -1

⇒ y = -2

∴ Values of (x, y, z) = (2, -2, 1).

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step-by-step explanation:

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