用换元法最简单.
令x/7=y/10=z/5=t,则x=7t,y=10t,z=5t
代入2x+3y-2z=34
2×7t+3×10t-2×5t=34
34t=34
t=1
x=7t=7 y=10t=10 z=5t=5
x=7 y=10 z=5