[tex]d+e-f=-3 \\
e=f+d+7 \\
f=2e-6 \\ \\
\hbox{substitute 2e-6 for f in the 2nd equation and solve for e:} \\
e=2e-6+d+7 \\
e=2e+d+1 \ \ \ |-2e \\
-e=d+1 \ \ \ |\times (-1) \\
e=-d-1 \\ \\
\hbox{substitute -d-1 for e in the 3rd equation and solve for f:} \\
f=2(-d-1)-6 \\
f=-2d-2-6 \\
f=-2d-8[/tex]
[tex]\hbox{substitute -d-1 for e and -2d-8 for f in the 1st equation and solve for d:} \\
d+(-d-1)-(-2d-8)=-3 \\
d-d-1+2d+8=-3 \\
2d+7=-3 \ \ \ |-7 \\
2d=-10 \ \ \ |\div 2 \\
d=-5 \\ \\ e=-d-1=-(-5)-1=5-1=4 \\ \\
f=-2d-8=-2 \times (-5)-8=10-8=2 \\ \\
\boxed{d=-5} \\ \boxed{e=4} \\ \boxed{f=2} \\
\hbox{answer D}[/tex]
