Fiona's Fashion Store is world renowned for its buttoned uniforms. A collection of 36 shirts and 42 jackets contains 842buttons. A collection of 6 shirts and 7 jackets contains 137buttons. Each shirt has the same number of buttons, and each jacket has the same number of buttons. How many buttons are there in a Fiona's Fashion shirt, and how many buttons are there in a jacket?

To solve the problem, what you must do is a system of two equations with two Ingonites that describe the problem.
 Let:
 x = number of shirt buttons.
 y = number of buttons on jackets.
 Writing the system:
 36x + 42y = 842
 6x + 7y = 137
 We observe that the system is linearly dependent, therefore, it can not be solved.
 However, the solution is to solve the system of two equations with two unknowns.
In order to solve it, the system must be linearly independent.