If `x+y=3 and x-y=1`, then the value of xy is

Options

A. 2
B. 3
C. 4
D. 1

Answer

To solve the problem where we have the equations \(x + y = 3\) and \(x - y = 1\), and we need to find the value of \(xy\), we can follow these steps:

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

### Step 2: Add the two equations
To eliminate \(y\), we can add Equation 1 and Equation 2:
\[ (x + y) + (x - y) = 3 + 1 \]
This simplifies to:
\[ 2x = 4 \]

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

### Step 4: Substitute \(x\) back into one of the equations to find \(y\)
We can substitute \(x = 2\) back into Equation 1:
\[ 2 + y = 3 \]
Now, solve for \(y\):
\[ y = 3 - 2 = 1 \]

### Step 5: Calculate \(xy\)
Now that we have both \(x\) and \(y\), we can find \(xy\):
\[ xy = 2 \times 1 = 2 \]

### Final Answer
Thus, the value of \(xy\) is \(2\).

---