If the numbers are a, b and c, then:
a+b+c=-2, so 3a+3b+3c=-6 (1)
3a+2b+c=9 (2)
b-c/2=10, b=10+c/2 (3)
(1)-(2)=b+2c=-15, b=-15-2c, therefore 10+c/2=-15-2c, 25=-5c/2, c=-(2/5)25=-10.
And b=10-10/2=5, and a=-2-(b+c)=-2-(5-10)=-2+5=3.
CHECK
a+b+c=3+5-10=-2 OK.
3a+2b+c=3×3+2×5-10=9 OK.
b-c/2=5-(-5)=5+5=10 OK.
SOLUTION: a=3, b=5, c=-10.