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2 years ago

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

Mathematics

1 answer:

snow_lady [41]2 years ago

4 0

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)

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