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

Answer 1

I would use elimination.

There are 3 ways to solve systems of linear equations, taking into account that there are 3 parameters (x, y, and z):

1. Represent them as planes and find their point of intersection.
2. Substitution.
3. Elimination.

all of them work, but method 3 is the most efficient since can be difficult to project 3d shapes into a piece of paper (method 1), or tedious to use multiple substitutions.

I would use gaussian elimination since it easily finds the solution to one of the variables.

1 -5 2 0
1 4 -1 12
2 -1 3 10

1 -5 2 0
0 9 -3 12
0 9 -1 10

1 -5 2 0
0 9 -3 12
0 0 2 -2

1 -5 2 0
0 1 -1/3 4
0 0 1 -1

there. z = -1

Answer 2

for the second row, the element in the last column should be 4/3

Answer 3

for the last matrix :-D

Answer 4

the disadvantage of elimination would be making mistakes in your arithmetic when doing these row operations. It's still perhaps the best method when working with more dimensions.

Answer 5

you can use cramer's rule, but have fun finding the determinant of a 3x3 matrix, 3 times.