How Does Gaussian Elimination Help Solve Systems of Equations?

[killersanta]

Homework Statement

Using Gaussian Elimination:

3x - 2 y = 5
6x-4y =7

The Attempt at a Solution

[ 3 -2 5]
[6 -4 7]

* top row by 1/3
[1 -2/3 5/3]

* Top row by -6, add to bottom row:
[0 0 -3]

So I get this:
[1 -2/3 5/3]
[0 0 -3]

How can 0y equal -3?

 

[Mark44]

Homework Statement

Using Gaussian Elimination:

3x - 2 y = 5
6x-4y =7

The Attempt at a Solution

[ 3 -2 5]
[6 -4 7]

* top row by 1/3
[1 -2/3 5/3]

* Top row by -6, add to bottom row:
[0 0 -3]

So I get this:
[1 -2/3 5/3]
[0 0 -3]

How can 0y equal -3?

It can't. What this says is that you have an inconsistent system - one that has no solution. Graphically, your system represents two parallel lines that don't intersect.

BTW, the plural of matrix is matrices, not matrix's. In English, plurals are not formed by adding 's to the end of the singular word.

 

[Rebooter]

Homework Statement

Using Gaussian Elimination:

3x - 2 y = 5
6x-4y =7

The Attempt at a Solution

[ 3 -2 5]
[6 -4 7]

* top row by 1/3
[1 -2/3 5/3]

* Top row by -6, add to bottom row:
[0 0 -3]

So I get this:
[1 -2/3 5/3]
[0 0 -3]

How can 0y equal -3?

Your understanding of Elimination is ok.

Remember there are 3 different types of matrices. Echelon Form A, B, C
(or 1, 2 and 3 depending how what your prof is using)
A is a unique solution for each variable, B has free variables, C has no solutions

You should brush up on this.

 

[HallsofIvy]

In fact, with the two equations 3x - 2 y = 5 and 6x-4y =7, if you divide the second equation by 2, you have 3x- 2y= 7/2. 3x- 2y cannot be equal to both 5 and 7/2. These represent two parallel lines in the plane. They never intersect so the system of equations has no solution.