Problem Solving with an augmented matrix

[trainee engineer]

Hi Everyone

I have been working on the problem below and keep getting negative values where I should only have positive ones.



I have to write a system of equations, each one representing the metal and the fourth to represent what is left over, to start with which I have done as follows, then translate into a matrix

$$\frac{5}{100}x_{1}+\frac{7}{100}x_{2}+\frac{2}{100}x_{3}+\frac{1}{100}x_{4}=\frac{22}{5}$$$$\frac{3}{100}x_{1}+\frac{6}{100}x_{2}+\frac{1}{100}x_{3}+\frac{2}{100}x_{4}=\frac{33}{10}$$$$\frac{4}{100}x_{1}+\frac{5}{100}x_{2}+\frac{3}{100}x_{3}+\frac{1}{100}x_{4}=\frac{19}{5}$$$$\frac{88}{100}x_{1}+\frac{82}{100}x_{2}+\frac{94}{100}x_{3}+\frac{96}{100}x_{4}=\frac{33}{10}$$

My matrix is as follows

$$\begin{bmatrix} 5 & 7 & 2 & 1\\ 3 & 6 & 1 & 2\\ 4 & 5 & 3 & 1\\ 88 & 82 & 94 & 96 \end{bmatrix}$$
I have tried to find both row echelon and reduced row echelon matrices and also an augmented matrix to solve the system of equations.
I would like to know if I have interpreted correctly or need to review my equations

Thank you

 

[Steven G]

Its hard to tell where/if you made a mistake if you don't share your work.
Where is your equation that states x1 + x2 + x3 + x4 =1??

 

[blamocur]

Where does your last equation come from?

 

[BigBeachBanana]

Where does your last equation come from?

The complement of the 3 previous rows. e.g 100-5-3-4=88

 

[trainee engineer]

Thank you. I just wanted to know if I was starting on the right track. I have since solved the problem using an upper triangle matrix to get the determinant.