Solution:

To determine whether the given pair of linear equations have unique solutions, no solution, or infinitely many solutions, we need to graphically represent them.

Step 1: Rewrite the given equations in slope-intercept form:

2x - 3y = 5

-3y = -2x + 5

y = (2/3)x - 5/3

3x + 4y = 1

4y = -3x + 1

y = (-3/4)x + 1/4

Step 2: Plot the lines:

To graph the first equation, we can plot two points on the line by choosing any two values of x and then solving for y:

x = 0, y = -5/3

x = 3, y = -1/3

Plot these points on the coordinate plane and draw a line through them.

To graph the second equation, we can plot two points on the line by choosing any two values of x and then solving for y:

x = 0, y = 1/4

x = 4/3, y = 0

Plot these points on the coordinate plane and draw a line through them.

Step 3: Analyze the intersection of the lines:

Now we need to analyze the intersection of the two lines we just plotted. There are three possibilities:

1. If the lines intersect at exactly one point, then the system has a unique solution.
2. If the lines are parallel and do not intersect, then the system has no solution.
3. If the lines coincide (i.e., they are the same line), then the system has infinitely many solutions.

Step 4: Determine the solution:

Looking at the graph, we can see that the two lines intersect at a single point. Therefore, the system has a unique solution.

Final Answer: The given pair of linear equations has a unique solution.

Unique solution. sorry I am not able to show the graph