1.
Call equations A, B, C, D and I guess D should be w-x+y-z=-6.
A-D: E: w+4x=15; x=(1/4)(15-w)
C+D: F: 4w-2z=-8; 2w-z=-4; z=2w+4
We now have x and z in terms of w.
From A, y=9-2w-3x+z=9-2w-(3/4)(15-w)+2w+4=7/4+3w/4; y=(1/4)(3w+7).
All the variables are in terms of w. We just need to take one equation to find w.
Using B, w=x+y+2z-10=(15-w)/4+(3w+7)/4+4w+8-10=(22+2w)/4+4w-2.
2w=11+w+8w-4; 7w=-7, so w=-1; x=4; y=1; z=2.
CHECK:
A: -2+12+1-2=9; B: 1+4+1+4=10; C: -3+4-1-2=-2; D: -1-4+1-2=-6. All OK.
2.
A: Multiply through by 24: 16x-6y+15z=0
B: Multiply through by 60: 12x+40y-15z=-420
C: Multiply through by 120: -72x+160y-105z=-600
A+B: 28x+34y=-420; D: 14x+17y=-210; 7A+C: 40x+118y=-600; E: 20x+59y=-300
10D-7E: -243y=-2100+2100, so y=0; x=-420/28=-15; 15z=240, z=16.
CHECK:
Original A: -10+10=0
Original B: -3-4=-7
Original C: 9-14=-5
All OK.