# Difference between revisions of "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,