Step 1: Clear the fractions in the first equation.
The first equation is $\frac{3x}{2} + \frac{5y}{3} = 7$. Multiply every term by 6, the LCM of 2 and 3, to remove the denominators.
\[ 9x + 10y = 42 \]
The second equation is already in a clean form:
\[ 9x + 10y = 14 \]
Step 2: Try to eliminate a variable by subtraction, the way we normally solve a pair of equations.
Both equations have exactly the same left hand side, $9x + 10y$. Subtract the second equation from the first:
\[ (9x + 10y) - (9x + 10y) = 42 - 14 \]
\[ 0 = 28 \]
Step 3: Read what this contradiction tells us.
The statement $0 = 28$ is never true, no matter what $x$ and $y$ are. This means there is no pair of values $(x, y)$ that can satisfy both equations at the same time.
When the elimination step wipes out both variables and leaves a false numeric statement, the system has no solution at all.
Step 4: Connect this to the type of system.
A system with no solution is called inconsistent. Geometrically, it means the two lines never meet, so they are parallel and distinct.
Final Answer:
The pair of equations has no solution, so the system is inconsistent, which corresponds to option (B).
\[ \boxed{\text{Inconsistent}} \]