# Method of Substitution vs. Method of Addition or Elimination for Systems of Equations

Please discuss the following:

- Explain why vectors QR and RQ are not equivalent.

- Explain when the elimination method for solving a system of equations is preferable to the substitution method. Give examples.

https://brainmass.com/math/linear-algebra/method-of-substitution-vs-method-of-addition-or-elimination-for-systems-of-equations-41902

#### Solution Preview

Point Q to Point R in vector space is the opposite of Point R to Point Q so no these are not equivalent .The scalar value is but the directions are opposite.

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 ...

#### Solution Summary

The pros and cons of the method of substitution in comparison to the method of addition or elimination for the systems of equations is discussed in detail. The reason for non-equivalence of vectors QR and RQ is also discussed. This is completed in about 400 words and includes examples of each method.