Let's examine the given system of linear equations:
- \( 2x - 7y = 4 \)
- \( 2x - 7y = -4 \)
Notice that both equations have the same left-hand side (\(2x - 7y\)). This implies that the two equations represent parallel lines with different constant terms on the right-hand side (4 and -4).
Since two parallel lines do not intersect, this system has no solution.
Therefore, the answer is 2 (no solution).