Question 1205687
this is a lengthy process, best solved by use of a gaussian elimination calculator, such as the one found at <a href = "https://onlinemschool.com/math/assistance/equation/gaus/" target = "_blank">https://onlinemschool.com/math/assistance/equation/gaus/</a>


the process is to have a 1 on each row for different variables on each row.


here's a picture of the process as it goes through row manipulation to achieve that effect.


<img src = "http://theo.x10hosting.com/2024/011901.jpg">


<img src = "http://theo.x10hosting.com/2024/011902.jpg">


<img src = "http://theo.x10hosting.com/2024/011903.jpg">


<img src = "http://theo.x10hosting.com/2024/011904.jpg">


<img src = "http://theo.x10hosting.com/2024/011905.jpg">


the whole idea is to make the matrix have a 1 in the position for each variable on individual rows.


the 4th display from the bottom shows you what i mean.


this is done through row manipulation.


here's a referemce.


<a href = "https://math.libretexts.org/Bookshelves/Applied_Mathematics/Applied_Finite_Mathematics_(Sekhon_and_Bloom)/02%3A_Matrices/2.02%3A_Systems_of_Linear_Equations_and_the_Gauss-Jordan_Method" target = "_blank">https://math.libretexts.org/Bookshelves/Applied_Mathematics/Applied_Finite_Mathematics_(Sekhon_and_Bloom)/02%3A_Matrices/2.02%3A_Systems_of_Linear_Equations_and_the_Gauss-Jordan_Method</a>


here's a youtube by patrickJMT that might help.


<a href = "https://www.youtube.com/watch?v=Ey62H_oaqoE" target = "_blank">https://www.youtube.com/watch?v=Ey62H_oaqoE</a>


patrick has several videos on the subject, as do other tutors on youtube.


the process is logical, but painful to execute.


i've tried it manually several times.
it's prone to errors and can lead you down dead ends, requiring you to start again.


try the calculator yourself to see how it works for you.


if you want to tackle it manually, pick a simple problem to start until you get the feel for it.


something with two rows and 2 variagles to solve, then maybe 3 rows with 3 variable to solve.


this one is more complex with 4 variables and 4 rows to solve.