When two linear expressions have different coefficients and constants, how many solutions do they have?

When considering two linear expressions, each can be represented in the form of equations, such as ( y = mx + b ) where ( m ) is the slope and ( b ) is the y-intercept. If the coefficients of the variables in these expressions differ, it implies that the slopes are not the same. When two lines have different slopes, they will intersect at exactly one point in a two-dimensional graph, which corresponds to a single unique solution for the system of equations represented by those linear expressions.

To explore further, if the two linear expressions were to have the same slope, there could be either no solutions (if the lines are parallel and distinct) or infinitely many solutions (if they are coincident). However, since the question specifies that the coefficients are different, we can conclude that they must intersect at one unique point.

Thus, the correct answer is that the two linear expressions have one solution. This key characteristic of differing slopes leading to a point of intersection underlines the principle behind solving systems of linear equations.