Question

​​​​​​​
Use the Gauss-Jordan method to solve each linear system. 3 x-9 y=24 7 x-21 y=50

Answer 1

Using the Gauss-Jordan method, the given system of linear equations is transformed into an inconsistent system, indicating that there are no solutions.

Step-by-step explanation:

To solve the linear system using the Gauss-Jordan method, we want to transform the augmented matrix that represents the system into reduced row-echelon form. Here is the system of equations we are working with:

1. 3x - 9y = 24
2. 7x - 21y = 50

We can start by setting up the augmented matrix:

[3 -9 | 24]

[7 -21 | 50]

Now, we want to make the leading coefficient of the first row a 1. We can divide the entire first row by 3, which gives us:

[1 -3 | 8]

[7 -21 | 50]

Next, we need to eliminate the x term from the second row. We can do this by subtracting 7 times the first row from the second row, leaving us with:

[1 -3 | 8]

[0 0 | -6]

However, we've reached an inconsistency. The second row now translates to the equation 0x + 0y = -6, which is not possible, indicating that there are no solutions to this system of equations or that the system of equations is inconsistent.