2x +3y=9 4x+6y=7 solve using Gauss-Jordan method to solve each system of equations

Answer:

To solve the system of equations using Gauss-Jordan elimination, we can write the augmented matrix and perform row operations to transform it into row echelon form.

The given system of equations:

2x + 3y = 9

4x + 6y = 7

Writing the augmented matrix:

[ 2 3 | 9 ]

[ 4 6 | 7 ]

Performing row operations:

1. Row 1 / 2 â Row 1:

[ 1 3/2 | 9/2 ]

[ 4 6 | 7 ]

2. Row 2 - 4 * Row 1 â Row 2:

[ 1 3/2 | 9/2 ]

[ 0 0 | -17 ]

3. Row 1 - (3/2) * Row 2 â Row 1:

[ 1 3/2 | 43/2 ]

[ 0 0 | -17 ]

4. Row 1 * 2/3 â Row 1:

[ 2/3 1 | 43/3 ]

[ 0 0 | -17 ]

5. Swap Row 1 and Row 2 for better readability:

[ 0 0 | -17 ]

[ 2/3 1 | 43/3 ]

6. Row 2 - (2/3) * Row 1 â Row 2:

[ 0 0 | -17 ]

[ 2/3 1 | 43/3 ]

7. (3/2) * Row 2 â Row 2:

[ 0 0 | -17 ]

[ 1 3/2 | 43/2 ]

8. Divide Row 2 by 3/2:

[ 0 0 | -17 ]

[ 1 1 | 43 ]

The augmented matrix is now in row echelon form. We can solve for the variables:

From Row 2, we have:

x + y = 43

Substituting this into Row 1 (or one of the original equations), we have:

0 = -17

This is contradictory, indicating the system has no solution. Thus, the system of equations is inconsistent and has no solution.