Question

X+ y + z = -3 3y - Z = 4 2x- y - 2z = -5

Answer 1

Answer:

• (-3, 1, -1)

Step-by-step explanation:

• x + y + z = -3  --> (1)
• 3y - z = 4   --> (2)
• 2x - y - 2z = -5 --> (3)

Add up (1) and (2)

• x + 3y + y + z - z = -3 + 4 ⇒ x + 4y = 1  --> (4)

Double (2) and subtract from (3)

• 2x - y - 2z - 2(3y - z) = -5 - 2(4) ⇒ 2x - y - 2z - 6y + 2z = -5 - 8
• 2x - 7y = -13 --> (5)

Double (4) and subtract (5)

• 2(x + 4y) - 2x + 7y = 2 + 13 ⇒ 2x + 8y - 2x + 7y = 15 ⇒ 15y = 15 ⇒ y = 1

Finding x

• x + 4(1) = 1 ⇒ x = 1 - 4  ⇒ x = -3

Finding z

• -3 + 1 + z = -3 ⇒ z = -1

So the answer is:

• (-3, 1, -1)