# Simultaneous Equations in 4 variables!

Algebra Level 2

Given that $$a,b,c,d$$ are real numbers such that

$a+b+c=5,$ $a+b+d=7,$ $a+c+d=11,$ $b+c+d=13,$

find the value of $$\displaystyle| abcd \displaystyle|$$.

Details and Assumptions

$$\displaystyle| n \displaystyle|$$ denotes the absolute value of $$n$$.

For example, $$\displaystyle| -3 \displaystyle|$$ $$= 3$$ and $$\displaystyle| 4 \displaystyle|$$ $$= 4$$.

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