Take the negatives out of the first equation: x+y+z=8. Divide the last equation through by 2: x+z=2. Substitute this in the previous equation: y+2=8, so y=6. Substitute y=6 in the second equation: -4x+24+5z=7, so -4x+5z=-17. We know x+z=2, so z=2-x. Substitute for z in the previous equation: -4x+10-5x=-17, so 9x=27 and x=3, and finally substitute this x to find z=2-3=-1. Check by substituting these values of x, y and z in the original equations.