Answer:
Option A ( 2, 2, 2)
Step-by-step explanation:
2x + 2y + z = 10 ------------(1)
3x - y + 3z = 10 ------------(2)
2x + 3y - 2z = 6
------------(3)
Equation (1) - equation (3)
(2x + 2y + z) - (2x + 3y - 2z) = 10 - 6
(2x - 2x) + (2y - 3y) + (z + 2z) = 4
-y + 3z = 4 --------------------(4)
Equation (1) × 3 - equation (2) × 2
3(2x + 2y + 2) - 2(3x - y + 3z) = 30 - 20
6x + 6y + 3z - 6x + 2y - 6z = 10
(6x - 6x) + (6y + 2y) + (3z - 6z) = 10
8y - 3z = 10 ----------------(5)
Now equation (4) × 8 + equation (5)
8(-y + 3z) + (8y - 3z) = 32 + 10
-8y + 2yz + 8y - 3z = 42
21z = 42
⇒ z = 2
Now we put z = 2 in equation (4)
-y + 3 × 2 = 4 ⇒ -y = 4 - 6
y = 2
From equation (1) 2x + 2 × 2 + 2 = 10
2x + 4 + 2 = 10
2x = 10 - 6 = 4 ⇒ x = 2
Option A ( 2, 2, 2) is the answer.
