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Directions of Vectors and Solving Systems of Equations by Elimination and Substitution

I am asking for assistance with the below questions:

1. Explain why vectors QR and RQ are not equivalent.
2. Explain in your own words when the elimination method for solving a system of equations is preferable to the substitution method.

I have attempted to answer the questions but am wishing to see if done correctly and am also looking for examples if possible. I vaguely understand the concept but am in need examples for clarification.

1 - Vectors are defined or measured by their magnitude and length. So for two vectors to be equivalent they in turn need to have the same length and direction. However, vectors QR and RQ are in opposite direction thereby causing them not to be equivalent.

2 - If there is a problem with a large number of equations and variables then the elimination method would be preferable to the substitution method. After all, it would break down the problem and/or equations in an easier manner.

Solution Preview

Dear student,

Your answer for the first question is perfectly right.
If you want to explain the same fact geometrically, You can add the following lines.

Vector PQ is the directed line segment formed by joining P to Q, i.e. the initial point for the vector PQ is P ...

Solution Summary

Directions of Vectors and Solving Systems of Equations by Elimination and Substitution are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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