Solve for w, x, y, z

x + 2y - z = 3

2x - y + z - w = - 3

y + 2z - w = - 7

x + 3y + 2z + 2w = 3

x = 1; y = 0; z = - 2 and w = 3.

Step-by-step explanation:

Given that,

1) x + 2y - z = 3

2) 2x - y + z - w = - 3

3) y + 2z - w = - 7

4) x + 3y + 2z + 2w = 3

now, from 1) z = x + 2y - 3 →→ (5)

from 2) w = 2x - y + z + 3

⇒w = 2x - y + x + 2y - 3 + 3 (from (5))

w = 3x + y →→ (6)

Now substitute (5) and (6) in 3), we get

y + 2 (x + 2y - 3) - (3x + y) = - 7

⇒ 4y - x = - 1 →→→ (7)

Now substitute (5) and (6) in 4), we get

x + 3y + 2 (x + 2y - 3) + 2 (3x + y) = 3

⇒ 9x + 9y = 9

⇒ x + y = 1 →→→ (8)

⇒ x = 1-y, substituting this in (7) gives 5y - 1 = - 1

⇒ y = 0 and x = 1

substituting these values in

(5) and (6) gives, z = - 2 and w = 3

⇒ x = 1; y = 0; z = - 2 and w = 3.