How do you solve using gaussian elimination or gauss-jordan elimination, 3x+2y = -93x+2y=−9, -10x + 5y = - 5−10x+5y=−5?

1 Answer
Eddie
Mar 16, 2017

See below

Explanation:

First create the augmented matrix:

((3,2),(-10,5))((-9),(-5))

For Gaussian elimination , we eliminate by combining rows to get a lower triangle matrix.

R2 to R2 + 10/3 R1
((3,2),(0,35/3))((-9),(-35))

Then back substitute, so from the second row:

35/3 y = - 35 implies y -3

From first row:

3x + 2y = - 9 implies x = (-9 - 2(-3))/(3) = -1

For Gauss-Jordan elimination , we row reduce to the identity matrix ie A mathbf x = mathbf b to I mathbf x = mathbf b'. So the first step can be the same:

R2 to R2 + 10/3 R1
((3,2),(0,35/3))((-9),(-35))

Then we can do this:
R1 to R1 - R2 cdot 6/35
((3,0),(0,35/3))((-3),(-35))

Finally we divide each row by its pivot, ie:

((3/3,0),(0,(35/3)/(35/3)))((-3/3),(-35/(35/3)))

implies ((1,0),(0,1))((-1),(-3))

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