Using complete sentences, explain which method you would use to solve the following system of equations and why. In your answer, include the solution to one of the variables and how you found it using the method you chose.

x - 5y + 2z = 0
x + 4y - z = 12
2x - y + 3z = 10

Help?

Question

Using complete sentences, explain which method you would use to solve the following system of equations and why. In your answer, include the solution to one of the variables and how you found it using the method you chose.

x - 5y + 2z = 0
x + 4y - z = 12
2x - y + 3z = 10

Help?

anonymous · Answer

I would use elimination(canceling out x) because it seems easy .

anonymous · Answer

I would just use substitution in which you multiply each equation by a certain value which then yields the same coefficient for only one variable in the system of equations and then you just add or subtract to get rid of it and do the same until you are down to only one variable which you then solve for.

anonymous · Answer

Just follow this website it has an example which you can use! http://www.mathwarehouse.com/algebra/planes/systems/three-variable-equations.php

anonymous · Answer

The coefficients of a system of equations can be interpreted as the matrix representation of a linear transformation. After constructing a matrix using the coefficients you can perform various invertible "elementary operations" that preserve the solution space and null space (rank and nullity). You then perform what is known as row reduction: http://planetmath.org/encyclopedia/GaussianElimination.html

anonymous · Answer

I should mention that you need to construct an augmented matrix. This is discussed in the article above.

anonymous · Answer

Reduced form: $$\left[ \begin {array}{cccc} 1&0&0&7\ 0&1&0&1 \ 0&0&1&-1\end {array} \right]   $$

anonymous · Answer

x = 7
y = 1
z = -1

anonymous · Answer

how did you get the answer z = -1 if you use the elimination method?