Answer:
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.
