how do you solve x+y=2000;6x+8y=14400 using gauss-jordan elimination medthod?
http://www.gregthatcher.com/Mathematics/GaussJordan.aspx
Add (-6 * row1) to row2
1 1 2000
0 2 2400
Divide row2 by 2
1 1 2000
0 1 1200
Add (-1 * row2) to row1
1 0 800
0 1 1200
I found that with Google. I just put in: Gauss Jordan Calculator. There were lots of them. I just picked the first one on the list.
To solve the given system of equations using the Gauss-Jordan elimination method, we can follow these steps:
Step 1: Write the augmented matrix for the system of equations.
[1 1 | 2000]
[6 8 | 14400]
Step 2: Apply row operations to transform the matrix into row-echelon form.
First, we want to create a zero below the first entry in the first column.
Row2 = Row2 - 6 * Row1
This operation eliminates the x term in the second equation.
New Matrix:
[1 1 | 2000]
[0 2 | 2400]
Step 3: Next, we want to make the coefficient of y in the second row equal to 1.
We can achieve this by multiplying the second row by 1/2.
Row2 = (1/2) * Row2
New Matrix:
[1 1 | 2000]
[0 1 | 1200]
Step 4: To create a zero above the entry in the second row, we can eliminate the x variable.
Row1 = Row1 - Row2
New Matrix:
[1 0 | 800]
[0 1 | 1200]
Step 5: The matrix is now in row-echelon form. The values in the rightmost column correspond to the solutions of the equations. Therefore, x = 800 and y = 1200.
So, the solution to the system of equations is x = 800 and y = 1200.