Introduction:
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 degree of a linear equation is always 1. In this context, the question asks about the possible number of solutions for any linear equation in two variables.

Explanation:
A linear equation in two variables represents a straight line on a Cartesian plane. The number of solutions to such an equation depends on the relationship between the coefficients and constants in the equation.

Case 1: Parallel Lines
If two linear equations have the same slope but different y-intercepts, they represent parallel lines. In this case, the lines will never intersect and the system of equations will have no solution. This can be represented by the equation 2x + 3y = 4 and 2x + 3y = 8.

Case 2: Coinciding Lines
If two linear equations have the same slope and the same y-intercept, they represent coinciding lines. In this case, the lines will overlap and have infinitely many points of intersection. This can be represented by the equation 2x + 3y = 4 and 4x + 6y = 8.

Case 3: Intersecting Lines
If two linear equations have different slopes, they represent intersecting lines. In this case, the lines will intersect at a single point, and the system of equations will have one solution. This can be represented by the equation 2x + 3y = 4 and 5x - 2y = 7.

Conclusion:
From the above cases, it is clear that a linear equation in two variables can have different numbers of solutions. It can have no solution (parallel lines), one solution (intersecting lines), or infinitely many solutions (coinciding lines). Therefore, the correct answer is option 'D' - an infinite number of solutions.