Previous Year Questions

We are given the following system of equations:

X - 2Y + 2Z = 16

X - Y + Z = 9

2X - 3Y - Z = 9

To find Y, we can solve these equations using elimination or substitution. Let's use elimination to simplify the process.

First, eliminate X by subtracting equation 2 from equation 1:

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

X - 2Y + 2Z - X + Y - Z = 7

-2Y + Y + 2Z - Z = 7

-Y + Z = 7 (Equation 4)

Next, eliminate Z between equation 2 and equation 3. Add equation 2 to equation 3:

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

X - Y + Z + 2X - 3Y - Z = 18

X + 2X - Y - 3Y + Z - Z = 18

3X - 4Y = 18 (Equation 5)

Now we have two new equations:

(4) -Y + Z = 7

(5) 3X - 4Y = 18

From equation 4, solve for Z:

Z = Y + 7

Substitute Z = Y + 7 into equation 2:

X - Y + (Y + 7) = 9

X - Y + Y + 7 = 9

X + 7 = 9

X = 2

Now substitute X = 2 into equation 5:

3(2) - 4Y = 18

6 - 4Y = 18

-4Y = 18 - 6

-4Y = 12

Y = -3

Option (b) is the correct answer.