Gauss – Jordan Elimination Method: Example 1. Solve the following system of linear equations using the Gauss-Jordan elimination method. The system of linear equations. 4x – 3y = 7 3x – 2y = 6. What is the next step?. Convert to a matrix of coefficients. 4x – 3y = 7 - PowerPoint PPT Presentation
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Gauss – Jordan Elimination Method: Example 1
Solve the following system of linear equations using the Gauss-Jordan elimination method
4x – 3y = 7
3x – 2y = 6
4x – 3y = 7
3x – 2y = 6
4 – 3 7
3 – 2 6
Now circle the pivot number.
4 – 3 7
3 – 2 6
1 – 3/4 7/4
3 – 2 6
(1/4) R1
R2
(– 3 ) R1
3 – 2 6
– 3 9/4 –21/4
0 1/4 3/4
1 – 3/4 7/4
0 1/4 3/4
R2 + (– 3) R1
1 – 3/4 7/4
0 1/4 3/4
1 – 3/4 7/4
0 1 3
( 4) R2
R1
(3/4) R2
1 – 3/4 7/4
0 3/4 9/4
1 0 4
1 0 4
0 1 3
R1 + (3/4) R2
1x + 0y = 3
0x + 1y = 4
1 0 3
0 1 4
Now simplify the system of equations.
x = 3
y = 4
1x + 0y = 3
0x + 1y = 4
Thus the solution is ( 3 , 4 )