If `x-y=3 and x+y=5`, what is the value of y?

Options

A. `-4`
B. `-2`
C. `-1`
D. `1`

Answer

To solve the equations \( x - y = 3 \) and \( x + y = 5 \) to find the value of \( y \), follow these steps:

### Step 1: Write down the equations
We have two equations:
1. \( x - y = 3 \) (Equation 1)
2. \( x + y = 5 \) (Equation 2)

### Step 2: Add both equations
To eliminate \( y \), we can add Equation 1 and Equation 2:
\[ (x - y) + (x + y) = 3 + 5 \]
This simplifies to:
\[ 2x = 8 \]

### Step 3: Solve for \( x \)
Now, divide both sides by 2 to find \( x \):
\[ x = \frac{8}{2} = 4 \]

### Step 4: Substitute \( x \) back into one of the original equations
We can substitute \( x = 4 \) into Equation 1:
\[ 4 - y = 3 \]

### Step 5: Solve for \( y \)
Now, isolate \( y \):
\[ 4 - 3 = y \]
Thus,
\[ y = 1 \]

### Conclusion
The value of \( y \) is \( 1 \).

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