SOURCE

http://doc.sagemath.org/html/en/constructions/linear_algebra.html


sage: var('a,b,c')(a, b, c)sage: eqn = [a+b*c==1, b-a*c==0, a+b==5]sage: s = 
solve(eqn, a,b,c); s[[a == (25*I*sqrt(79) + 25)/(6*I*sqrt(79) - 34),  b == 
(5*I*sqrt(79) + 5)/(I*sqrt(79) + 11),  c == 1/10*I*sqrt(79) + 1/10], [a == 
(25*I*sqrt(79) - 25)/(6*I*sqrt(79) + 34),  b == (5*I*sqrt(79) - 5)/(I*sqrt(79) 
- 11),  c == -1/10*I*sqrt(79) + 1/10]]


eqn = [a+b*c==1, b-a*c==0, a+b==5]

Is not a linear system of 3 equations for 3 unknowns, if c is asked. 

(only if c is a fixed symbolic constant, these are 3 linear equations for 2 
unknowns)

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