Find the value of Y, if X− 2Y + 2Z = 16, X − Y + Z = 9 and 2X − 3Y − Z = 9.
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Correct answer: B
Explanation
The correct answer is option 2 i.e. - 3.
X - 2Y + 2Z = 16 .....(1)
X - Y + Z = 9 .....(2)
2X - 3Y - Z = 9 .....(3)
Subtracting Equation (2) from Equation (1),
⇒ -Y + Z = 7 .....(4)
Multiplying Equation (2) by 2,
⇒ 2X - 2Y + 2Z = 18 .....(5)
Subtracting Equation (3) from Equation (5),
Y + 3Z = 9 .....(6)
Adding Equation (4) and Equation (6),
⇒ 4Z = 16
⇒ Z = 4
Substitute the value of Z into Equation (4),
-Y + 4 = 7
⇒ Y = -3
Therefore, the value of Y is -3.