Consistency of the System of Equations
There are two equations given:
1. 3/2x + 5/3y - 7 = 0
2. 9x - 10y - 14 = 0

Checking for Consistency
To determine if the system of equations is consistent, we need to analyze the slopes of the lines represented by the equations. If the slopes are different, the lines intersect at a single point, making the system consistent. If the slopes are the same, the lines are parallel and the system is inconsistent.

Calculating the Slopes
1. Equation 1: 3/2x + 5/3y - 7 = 0
Slope = -3/2 divided by -5/3 = 9/10
2. Equation 2: 9x - 10y - 14 = 0
Slope = -9 divided by -10 = 9/10

Analysis of the Slopes
The slopes of both equations are the same, which means the lines represented by the equations are parallel. Since parallel lines never intersect, the system of equations is inconsistent.

Conclusion
In this case, the system of equations is inconsistent because the lines represented by the equations are parallel. This means there is no solution that satisfies both equations simultaneously.