Eliminate x by taking two equations at a time and combining them in the the right parts.
For example, taking the first two equations, we can eliminate x by subtracting 2 times the second equation away from the first:
(2x - 5y + 7z) - 2 (x - 3y + 4z) = 6 - 2×3
(2x - 2x) + (-5y + 6y) + (7z - 8z) = 6 - 6
y - z = 0
Similarly, take 3 times the second equation from the third:
(3x - 8y + 11z) - 3 (x - 3y + 4z) = 11 - 3×3
(3x - 3x) + (-8y + 9y) + (11z - 12z) = 11 - 33
y - z = -22
But these two new equations say 0 = -22, which is not true. So there is no solution to this system.
