Answer :
[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]
[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]
