For the given pair of equations, two statements are given below - one labelled Assertion (A) and the other labelled Reason (R). Read the statements carefully and choose the option that correctly describes statements (A) and (R).
`(2)/(x)+5y=15`
`(3)/(x)+6y=7`
Assertion (A): The given pair of equations can be reduced to a pair of linear equations in two variables
Reason (R): In the given equations, y can be substituted by `(1)/(p)`

Options

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

Answer

To solve the problem, we need to analyze the given equations and the statements made in the assertion and reason.

### Given Equations:
1. \(\frac{2}{x} + 5y = 15\)
2. \(\frac{3}{x} + 6y = 7\)

### Step 1: Rewrite the Equations
To analyze these equations, we can introduce a new variable for \(\frac{1}{x}\). Let's denote:
\[ p = \frac{1}{x} \]
Then we can rewrite the equations in terms of \(p\).

### Step 2: Substitute \(p\) into the Equations
Now, substituting \(p\) into the equations:
1. The first equation becomes:
\[ 2p + 5y = 15 \]
2. The second equation becomes:
\[ 3p + 6y = 7 \]

### Step 3: Analyze the New Equations
Now we have a new pair of equations:
1. \(2p + 5y = 15\)
2. \(3p + 6y = 7\)

These equations are now linear in terms of the variables \(p\) and \(y\).

### Step 4: Check the Assertion and Reason
- **Assertion (A)**: The given pair of equations can be reduced to a pair of linear equations in two variables.
- This is **True** because we have successfully rewritten the equations in terms of \(p\) and \(y\), which are linear.

- **Reason (R)**: In the given equations, \(y\) can be substituted by \(\frac{1}{p}\).
- This is **False** because the substitution of \(y\) as \(\frac{1}{p}\) does not directly relate to the original equations. The equations are already linear in \(p\) and \(y\) without needing to express \(y\) in terms of \(p\).

### Conclusion
The correct option that describes the statements is:
- Assertion (A) is True.
- Reason (R) is False.