Assertion (A): The graph of the linear equation 2x – y = 1 passes through the point (2, 3).
Reason (R): Every point lying on the graph is not a solution of 2x – y = 1.

To determine whether the assertion (A) is true or false, we need to analyze the given linear equation and verify if the point (2, 3) lies on the graph.

Analysis:
The given linear equation is 2x – y = 1.

Step 1: Representing the linear equation in slope-intercept form:
To find the slope-intercept form, we can rewrite the equation by isolating 'y' on one side of the equation.
2x – y = 1
-y = -2x + 1
y = 2x - 1

Therefore, the equation can be rewritten as y = 2x - 1, which is in the form y = mx + c, where 'm' represents the slope and 'c' represents the y-intercept.

From the equation y = 2x - 1, we can observe that the slope is 2 and the y-intercept is -1.

Step 2: Graphing the linear equation:
To graph the linear equation, we need to plot the y-intercept and use the slope to find additional points on the line.

The y-intercept is the point where the line intersects the y-axis. In this case, the y-intercept is (0, -1).

Using the slope, we can find additional points on the line. The slope of 2 means that for every 1 unit increase in x, there is a corresponding 2 unit increase in y. Similarly, for every 1 unit decrease in x, there is a corresponding 2 unit decrease in y.

Step 3: Verifying if the point (2, 3) lies on the graph:
To check if the point (2, 3) lies on the graph, we substitute the values of x = 2 and y = 3 into the equation y = 2x - 1.

y = 2(2) - 1
y = 4 - 1
y = 3

The y-coordinate obtained by substituting x = 2 and y = 3 satisfies the equation y = 2x - 1. Therefore, the point (2, 3) lies on the graph of the linear equation 2x – y = 1.

Conclusion:
The assertion (A) is true because the point (2, 3) lies on the graph of the linear equation 2x – y = 1. The reason (R) is false because every point lying on the graph of the equation is a solution of 2x – y = 1.