Assertion (A) : `x=3` and `y=1` is the solution for the lines `x+5y=3` and `x-y=1`
Reason (R ) : The point of intersection of two lines in a graph is the common solution for both the lines represented by the equations.

Options

A. Both A and R are true and R is the correct explanation for A.
B. Both A and R are true and R is not correct explanation for A.
C. A is true but R is false
D. A is false but R is true

Answer

To determine the validity of the assertion (A) and the reason (R), we will evaluate both statements step by step.

### Step 1: Verify the Assertion (A)
The assertion states that \( x = 3 \) and \( y = 1 \) is a solution for the equations \( x + 5y = 3 \) and \( x - y = 1 \).

1. **Substituting into the first equation**:
\[ x + 5y = 3 \]
Substitute \( x = 3 \) and \( y = 1 \):
\[ 3 + 5(1) = 3 \implies 3 + 5 = 3 \implies 8 = 3 \quad \text{(False)} \]

2. **Substituting into the second equation**:
\[ x - y = 1 \]
Substitute \( x = 3 \) and \( y = 1 \):
\[ 3 - 1 = 1 \implies 2 = 1 \quad \text{(False)} \]

Since both equations do not hold true for \( x = 3 \) and \( y = 1 \), the assertion (A) is **false**.

### Step 2: Verify the Reason (R)
The reason states that the point of intersection of two lines in a graph is the common solution for both the lines represented by the equations.

1. **Understanding the reason**:
- The point of intersection of two lines represents the values of \( x \) and \( y \) that satisfy both equations simultaneously.
- This is a fundamental property of linear equations in two variables.

Since this statement is true based on the properties of linear equations, the reason (R) is **true**.

### Conclusion
- Assertion (A) is **false**.
- Reason (R) is **true**.