Note that , , and denote the amount of money Uno, Duo, and Traea owe, respectively.
We first express the three statements (1) "All together they owe $600", (2) "Duo owes $200 more than Uno", and (3) "Uno and Duo combined owe as much as Traea" as linear equations in , , and :
This system can be rewritten as
Then, the coefficient matrix can be formed by reading off the coefficients of each variable in each row. For the constant vector , we keep the same values:
Therefore, we find that
Note that the rows of the matrix and vector may be freely permuted without affecting the system; thus, for instance,
is also a valid answer.