To solve the given system of linear equations by inspection, we can look at the two equations:
- \( 2x - 7y = 4 \)
- \( 2x - 7y = -4 \)
Notice that the left-hand sides of both equations are identical (\(2x - 7y\)). This means the lines represented by both equations are parallel if their right-hand sides differ. Here, the right-hand sides are \(4\) and \(-4\). Since these constants are different, the two lines will never intersect.
Thus, there is no solution to this system of equations.
Therefore, the answer is 2 (no solution).