1) x+y+z=6,
2) 2x+y-3z=-5,
3) 4x-5y+z=-3.
3(1)+(2): 5x+4y=18-5=13 (4)
3(3)+(2): 14x-14y=-14, x-y=-1, y=x+1 (5), substitute for y in (4): 5x+4x+4=13, 9x=9, x=1 so y=2.
Substitute x=1 and y=2 in (1): 1+2+z=6, so z=3.
Each equation represents a plane, two planes intersect on a line and two lines intersect at the point (1,2,3).