Answer :
This is a high school mathematics problem about solving a system of linear equations. The solution involves either substitution, elimination or a matrix method. The solution is presented as an ordered triple (d, e, f).
The topic at hand is the system of linear equations which given as the following: 7d + 28e - 28f = 105, -44 - e + 46f = 2 and 4d + 14e - 23f = 38. The goal is to find an ordered triple solution which is (d, e, f). To find the solution, you can use substitution, elimination or a matrix method. However, as the equations look quite complex, matrix method can be convenient. With this method, you can create a matrix from the coefficients of the variables and then use Gaussian elimination or another matrix method to solve it. It's a systematic way of simplifying the system into a form where you can easily see the solution. By performing these calculations, you will find a unique solution (d, e, f) that satisfies all three equations.
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