Answer:
(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).
