Question

How do you solve using gaussian elimination or gauss-jordan elimination, `x+2y=7` , `3x-2y=-3`?

Answer 1

`x=1` and `y= 3`

Explanation:

Rewrite this system in matrix form
`|1 2]` `[x]` `= [7]`
`|3 -2]` `[y]` `[-3]`

Now we want to put this matrix in triangular form. This amounts to eliminating y for instance.

Adding both rows yields
[1 2] [x] = [7]
[4 0] [y] [4]

In this form, you see that triangular means one equation will have all zero matrix element except one. In our case the bottom equation reads

`4x= 4`
The equation right above will have two non-zero matrix elements. Using the solution from the bottom equation, you can plug this solution into the equation above to get
`x + 2y = 7`
`1 + 2y = 7`
or `2y = 6`
That is `y = 3`

Check
`x+ 2y = 1 + 2*3= 7`
`3x - 2y = 3 - 6 = -3`

That method only becomes efficient when you have more than two variables.