Solve the system

Question

x1+x2=-4

x2+x3=-4

x3+x4=4

x1+x4=4

 

 

Answer 1

Dalia,

 

There is no unique solution to this set of equations.  If you examine equations 1 & 2, subtracting 2 from 1 gives:

 

x1 - x3 = 0 ⇒ x1 = x3.  If you use this result you see that the last 2 equations are not independent and offer no unique solution.

 

Several possible solutions are immediately obvious, we can let x1 = x3 = 0, in which case x2 =-4 and x4 = +4.

 

Another solution would be to let x1 = x3 = -4, then x2 =0 and x4 = +8, or we could let x1 = x2 = x3 = -2, then 

x4 =6.  There are an infinite number of other possible solutions.