If x=a, y= b is the solution of the equation `x-y =2 and x+y= 4`, then the values of a and b are, respectively

Options

A. 3 and 5
B. 5 and 3
C. 3 and 1
D. `-1` and 3

Answer

To solve the 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: Substitute \( x \) and \( y \) with \( a \) and \( b \)
We start by substituting \( x \) with \( a \) and \( y \) with \( b \) in both equations:

1. From the first equation:
\[ a - b = 2 \quad \text{(Equation 1)} \]

2. From the second equation:
\[ a + b = 4 \quad \text{(Equation 2)} \]

### Step 2: Add the two equations
Next, we add Equation 1 and Equation 2 together:

\[ (a - b) + (a + b) = 2 + 4 \]

This simplifies to:

\[ 2a = 6 \]

### Step 3: Solve for \( a \)
Now, we can solve for \( a \):

\[ a = \frac{6}{2} = 3 \]

### Step 4: Substitute \( a \) back into one of the equations to find \( b \)
Now that we have \( a = 3 \), we can substitute this value back into Equation 2 to find \( b \):

\[ 3 + b = 4 \]

### Step 5: Solve for \( b \)
Now, solve for \( b \):

\[ b = 4 - 3 = 1 \]

### Conclusion
Thus, the values of \( a \) and \( b \) are:

\[ a = 3, \quad b = 1 \]