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.

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.

4x+y=12 (1)
x-y=8(2)
4x+y=12
x-y=8
5x/5 = 20/5
X=4
4(4) =y - 12
16+y = 12
Y =4
I think this would be an example of eliminationmethodfor solving a system of equations however I am unsure how it would transfer to substitutionmethod thus I am needing assistance. I am needing this to be illustrated if you wi

Compare the advantages and disadvantages of substitution and eliminationmethods with the matrix method to solve systems of linear equations and the relationship these have with matrix method solving.

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

Please help with the following problems.
There are three methods to solving Linear Systems with two Equations. They are the Graph method, the Eliminationmethod, and the Substitutionmethod. When would you use each method? What makes each method better than the other methods?

1. Solve the following system of equations using the Substitutionmethod:
5X-7Y= - 18
4X+3Y= 20
2. Solve the following system of equations using the eliminationmethod:
2X-3Y=12
-2X+3Y=12
Solution: Computation of the Equations
2X-3Y =12
-2X+3Y =12
3. A total of $80,000 is invested in two funds paying 2.3% and 3.1

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 eliminationmethodfor solving a system of equations is preferable to the substitutionmethod.
I have attempted to answer the questions but am wishing to see if done correctly

1. Explain why vectors QR and RQ are not equivalent.
2. Explain when the eliminationmethodfor solving a system of equations is preferable to the substitutionmethod.
It is extremely important for you to show your work. This helps me immensely, as I am much better working backwards when it comes to math problems and soluti