If `x-y=2,y-z=4, and x-y-z=-3`, then y=

Options

A. 1
B. 5
C. 9
D. 11

Explanation

To solve the equations given in the problem, we will follow these steps:

### Step 1: Write down the equations
We have the following equations:
1. \( x - y = 2 \) (Equation 1)
2. \( y - z = 4 \) (Equation 2)
3. \( x - y - z = -3 \) (Equation 3)

### Step 2: Rearrange Equation 1
From Equation 1, we can express \( x \) in terms of \( y \):
\[ x = y + 2 \]

### Step 3: Rearrange Equation 2
From Equation 2, we can express \( z \) in terms of \( y \):
\[ z = y - 4 \]

### Step 4: Substitute \( x \) and \( z \) into Equation 3
Now, we substitute \( x \) and \( z \) into Equation 3:
\[ (y + 2) - y - (y - 4) = -3 \]

### Step 5: Simplify the equation
Let's simplify the left-hand side:
\[ y + 2 - y - y + 4 = -3 \]
This simplifies to:
\[ 2 + 4 - y = -3 \]
\[ 6 - y = -3 \]

### Step 6: Solve for \( y \)
Now, we can solve for \( y \):
\[ -y = -3 - 6 \]
\[ -y = -9 \]
\[ y = 9 \]

### Final Answer
Thus, the value of \( y \) is:
\[ \boxed{9} \]