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.

2x + y + z = -7
x - 3y + 4z = -14
x - 2y - 3z = -11

Answer 1

To solve this system, I would use Gauss-Jordan Elimination.

Answer 2

or determinants

Answer 3

or you could row reduced the augmented matrix which is [A b] where A is the coefficient matrix of the systems of equations and b is the 1x1 matrix.

Answer 4

a 1x1 matrix?

Answer 5

z=0,y=3 and x=-5

Answer 6

So all those lines intersect at (0,3,-5)

Answer 7

that's the solution :-D

Answer 8

Another way of doing it would be to solve for x
Ax=b
\[x = A^{-1}*b\]

Answer 9

You could also use cramer's rule

Answer 10

I chose the row reduction method because I found it easy

Answer 11

I don't like finding the determinants of 3x3 matrices or graphing 3 dimensional curves :-P

Answer 12

I don't think those are curves, they look more like planes.

Answer 13

I argee that cramer's rule is tedious though

Answer 14

planes aren't so fun to graph on a sheet of paper either :-P

Answer 15

But that is if you limit your imagination. I can graph planes on paper.