Me i beg you i really need !
assignment: solve by elimination

X=number of adults
y=number of children

a)
x+y=8                 
12x+10y=86

b
-12*(x+y=8)                      (the equation "x+y=8" is multiplied by -12)
 12x+10y=86  

         -2y=-10                             ⇒y=-10/-2=5

-10*(x+y=8)                    (the equation "x+y=8" is multiplied by -10)
 12x+10y=86

      2x=6                                     ⇒ x=6/2=3

c)
solution: the number of adults is 3, the number of children is 5, this solution is right because. 

Check:
adults + children=3+5=8 people.
adult spent =3 adults * ($12/adult)=$36
children spent=5 children *($10/child)=$50
adult spent + children spent=$36+$50=$86

Ab=dc ac=de ad=bce i hope this !