Matrices in Row-Echelon Form/Gaussian Elimination

[xxMsJojoxx]

I cannot figure out how to solve the 2nd row for Row-Echelon Form.

-- How you know which equation to arrange as the second row?

For example, the equation is 2x-3y = -9 AND 5x+4y=58. So the augmented matrix form is:


Then to reduce to row-echelon form...
For the 1st row, I multiplied by 1/2., to get:

But I'm stuck at the second row. I tried multiplying the 1st row by -5, then adding to row 2 to get: . This is obviously wrong.

Are there any tips on to know which equation to select as 1st, and what number to multiply the 1st row by, to get the second row in the matrix?

 

[Steven G]

When you multiplied 1 -3/2 -9/2 by -5 you made a mistake. Even you said that you made a mistake so why not fix it??

Whoever told you that your non-zero leading entry should be a 1 prior to the last step has mislead you in my opinion. Getting that leading 1 early on leads to the possibility of having to deal with fractions. If you leave the non-zero entry as it is until the last step you will not have any fractions until the end. At thet point you are done so fractions are not a big deal. Of course if you matrix starts out with fractions then multiply each row my a non zero that makes the fractions disappear.