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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Step-by-step explanation:
