If two linear systems have exactly the same solutions, then they have the same augmented matrix.True or False? I think it would be false? Why?

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- Feb 19th 2013, 05:01 PMCivy71True or False
If two linear systems have exactly the same solutions, then they have the same augmented matrix.

**True or False**? I think it would be false? Why? - Feb 20th 2013, 03:59 AMveileenRe: True or False
False.

(S1):

$\displaystyle x+y=5$

$\displaystyle x-y=3$

(S2):

$\displaystyle 2x+2y=10$

$\displaystyle 2x-2y=6$

(S3):

$\displaystyle 3x-2y=10$

$\displaystyle x+5y=9$