If x = a, y = b is the solution of the pair of equation x - y = 2 and x + y = 4 then the value of 'a' and 'b' are respectively.

Options

A. 1,3
B. 2,3
C. 3,1
D. 2,5

Answer

To solve the given pair of equations \( x - y = 2 \) and \( x + y = 4 \) for the values of \( a \) and \( b \) where \( x = a \) and \( y = b \), we can follow these steps:

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

### Step 2: Substitute \( a \) and \( b \)
Since we know that \( x = a \) and \( y = b \), we can substitute these into the equations:
1. \( a - b = 2 \) (Equation 1)
2. \( a + b = 4 \) (Equation 2)

### Step 3: Solve the equations using elimination
To eliminate \( b \), we can add both equations:
\[ (a - b) + (a + b) = 2 + 4 \]
This simplifies to:
\[ 2a = 6 \]
Now, divide both sides by 2:
\[ a = 3 \]

### Step 4: Substitute \( a \) back to find \( b \)
Now that we have \( a = 3 \), we can substitute this value back into one of the original equations to find \( b \). Using Equation 1:
\[ 3 - b = 2 \]
Now, solve for \( b \):
\[ 3 - 2 = b \implies b = 1 \]

### Step 5: Final values
Thus, the values of \( a \) and \( b \) are:
\[ a = 3 \quad \text{and} \quad b = 1 \]

### Conclusion
The final answer is:
\[ \text{Hence, } a = 3 \text{ and } b = 1 \]