Answer:Let’s rearrange the first and third equations in terms of  a :
⇒a+b=8⇒a=8−b  (i) 
and
⇒a+c=13⇒a=13−c(ii) 
Then, let’s equate  (i)  and  (ii) :
⇒8−b=13−c⇒b=c−5(iii) 
Now, let’s use the second and fourth equations to find expressions for  b  and  c :
⇒c−d=6⇒c=6+d(iv) 
and
⇒b+d=8⇒b=8−d(v) 
Let’s equate  (iii)  and  (v) :
⇒c−5=8−d⇒c=13−d(vi) 
We can now equate  (iv)  and  (vi) :
⇒6+d=13−d⇒2d=7∴d=72 
Let’s substitute this value of  d  into  (iv)  and  (v) :
∴c=6+(72)=192 
and
∴b=8−(72)=92 
We can use either  (i)  or  (ii)  to find  a .
Let’s try using  (i) :
∴a=8−(92)=72 
Therefore, the solutions to the system of equations is  a=72 ,  b=92 ,  c=192 , and  d=72 .
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