# Systems of Equations : Real World Situations and Solving Determinants

1. In real-world situations, what is the advantage of using the Method of Substitution to solve a system of equations rather than using the Method of Addition?

2. When solving a 3x3 determinant, we broke the determinant down into a sequence of 2x2 determinants, remembering to alternate the signs of the leading coefficients in front of these smaller determinants. By extension, how might you calculate a 4x4 determinant?

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#### Solution Preview

1. In real-world situations, what is the advantage of using the Method of Substitution to solve a system of equations rather than using the Method of Addition?

Solution:

Both methods aim to solve the system of equations by eliminating (at least) one variable at a time until there exists only one variable remaining. Usually, if the coefficients of one variable in a pair of equations are the same or multiple of the other, the method of addition would be considered a more favorable technique than the method of substitution. But, the difficulty of using the addition method occurs when both coefficients need to be manipulated - using the Least Common Multiple (LCM), for example. Especially, in real-world situations where both coefficients of one variable in each pair of equations might be a large number or a non-integer, this would make LCM inefficient to simplify the ...

#### Solution Summary

For real-life situations, the advantages of using the Method of Substitution to solve a system of equations rather than using the Method of Addition are discussed.

The solving of determinants for larger matrices by breaking them down into smaller ones is discussed in terms of a general algorithm.

The solution is detailed and well presented.