Thread: 2 by 2 gaussian elimination help...wtf is this q asking?

Is this a possible gaussian elimination. It is asked in a genuine question for gaussian elimination btw.

2x + 3y = 5
6x + 9y = 15

As a matrix it looks like

2 3 |5
6 9 |15

But when you do: row 2- 3*row 1
you get 0 0 0 in the bottom row and now way of working out the x & y values......am i missing something here?

Hello, Latkan!

Your work is correct.

If you get a row of zeros (all the way across), there is an infinite number of solutions.

Look again and you'll see that the two given equations are equivalent.
The second equation is merely 3 times the first.
(They gave us the same equation twice!)
There's not enough information for a unique solution.

ahh yes i thought as much however another question is asking a similar thing but this time both the x and y values are equal to 0 but the answer is not zero:

2x + 3y = 1
6x + 9y = 5

as you can see

2 3 | 1
6 9 | 5

row 2- 2*row 1 = 0 0 3

so 0x + 0y = 3???? this cannot be true. So does this mean that the second row is null and tht there are an infinite number of solutions again?

If you get something like "0x + 0y = 3" then that means that there are no solutions.

But I think you meant row 2- 3*row 1 = 0 0 2

thnx i realised it was a no solution once i looked over my workings.