If `x+y=2500` and `x-y=2500` then the value of `x` is:

Options

A. 2500
B. 5000
C. 3000
D. 4000

Answer

To solve the equations \( x + y = 2500 \) and \( x - y = 2500 \) for the value of \( x \), we can follow these steps:

### Step 1: Write down the equations
We have two equations:
1. \( x + y = 2500 \) (Equation 1)
2. \( x - y = 2500 \) (Equation 2)

### Step 2: Add the two equations
To eliminate \( y \), we can add Equation 1 and Equation 2 together:
\[ (x + y) + (x - y) = 2500 + 2500 \]

### Step 3: Simplify the left-hand side
On the left-hand side, \( y \) cancels out:
\[ x + y + x - y = 2x \]
So we have:
\[ 2x = 5000 \]

### Step 4: Solve for \( x \)
Now, we divide both sides by 2 to find \( x \):
\[ x = \frac{5000}{2} \]
\[ x = 2500 \]

### Conclusion
The value of \( x \) is \( 2500 \).

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