# Science:Math Exam Resources/Courses/MATH152/April 2015/Question B 1 (a)/Solution 1

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.