Assertion (A): A linear equation in two variables has infinitely many solutions.
Reason (R): A linear equation 3x + 5y = 2 has a unique solution.

Explanation:

What is a linear equation in two variables?
A linear equation in two variables is an equation that can be written in the form ax + by = c, where a, b, and c are constants, and x and y are variables. The values of x and y that satisfy the equation are called solutions.

Infinitely Many Solutions:
A linear equation in two variables can have three possible scenarios:

1. No Solution: If the coefficients of x and y in the equation are such that their ratio is not the same as the ratio of the constant term to the coefficient of either variable, then the equation will have no solution. For example, 2x + 3y = 7 and 4x + 6y = 9 have no solution.

2. Unique Solution: If the coefficients of x and y in the equation are such that their ratio is the same as the ratio of the constant term to the coefficient of either variable, then the equation will have a unique solution. For example, 2x + 3y = 7 and 6x + 9y = 21 have a unique solution.

3. Infinitely Many Solutions: If the coefficients of x and y in the equation are such that their ratio is the same as the ratio of the constant term to the coefficient of either variable, and the constant term is also the same, then the equation will have infinitely many solutions. For example, 3x + 5y = 2 and 6x + 10y = 4 have infinitely many solutions.

Explanation of Assertion and Reason:
The assertion states that a linear equation in two variables has infinitely many solutions, while the reason argues that a specific linear equation, 3x + 5y = 2, has a unique solution.

The reason is incorrect because the equation 3x + 5y = 2 represents a line on the coordinate plane. A line in the coordinate plane can have infinitely many points on it, which means it has infinitely many solutions. Therefore, the reason is invalid.

The assertion is correct because a linear equation in two variables can have infinitely many solutions if its coefficients and constant term satisfy the conditions mentioned earlier. The specific equation given in the reason does not contradict the assertion.

Conclusion:
In conclusion, the assertion that a linear equation in two variables has infinitely many solutions is correct. The reason provided, which claims that the equation 3x + 5y = 2 has a unique solution, is incorrect. A linear equation can have no solution, a unique solution, or infinitely many solutions depending on the coefficients and constant term of the equation.

A is true, but R is false.