To solve the given system of linear equations by inspection, we can look at the two equations:
- \( 2x - 7y = 4 \)
- \( 2x - 7y = -4 \)
We can see that both equations have the same left-hand side \( 2x - 7y \). This indicates that both equations represent the same line if they were equal to the same number. However, the right-hand sides of the equations are not equal (4 and -4).
Since the left-hand sides are equal but the right-hand sides are different, we can conclude that the lines represented by these equations are parallel. Parallel lines do not intersect, which means there are no solutions to this system of equations.
Thus, the answer is 2 for no solution.