# Method of Substitution vs. Method of Addition or Elimination for System of Equations 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 3 x 3 determinant, we broke the determinant down into a sequence of 2 x 2 determinants, remembering to alternate the signs of the leading coefficients in front of these smaller determinants. By extension, how might you calculate a 4 x 4 determinant?

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#### Solution Preview

Addition (Elimination) usually simplifies the equation manipulation and works as long as the determinant of the equation matrix is non-zero. Any good linear algebra book should have plenty of examples to work from for you. Or go to Wolfram and look at linear equations. Elimination is usually easier than substitution and more reliable. Fewer steps means less room for error

A system like

3x + 2y =10

9x + 4y = 20

is easy to solve by elimination, and requires more steps if we use substitution.

In a system, if one equation is linear and the other is quadratic, then the elimination method does not work. So we have to use the substitution method to solve the system.

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#### Solution Summary

The method of substitution is contrasted with the method of addition (or elimination). Solving determinants using the determinants of smaller matrices is also discussed.