Find the value of Y, if X− 2Y + 2Z = 16, X − Y + Z = 9 and 2X − 3Y − Z = 9.

Correct option is B

Given:

X - 2Y + 2Z = 16.......(1)

X - Y + Z = 9............(2)

2X - 3Y - Z = 9 .........(3)

Solution:

Subtract equation (2) from equation (1):

(X - 2Y + 2Z) - (X - Y + Z) = 16 - 9

-Y + Z = 7 ---(4)

Multiply equation (2) by 2 and subtract it from equation (3):

(2X - 3Y - Z) - 2(X - Y + Z) = 9 - 2(9)

(2X - 3Y - Z) - (2X - 2Y + 2Z) = 9 - 18

-Y - 3Z = -9 ---(5)

Subtract equation (5) from equation (4):

(-Y + Z) - (-Y - 3Z) = 7 - (-9)

4Z = 16

Z = 4

Substituting Z = 4 in equation (4):

-Y + 4 = 7

-Y = 3

Y = -3

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