SOLUTION: For the following systems of equations in echelon form, tell how many solutions there are in nonnegative integers. x

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Question 976765: For the following systems of equations in echelon form, tell how many solutions there are in nonnegative integers. x - 7y+4z = 75; 2y+7z=60.
Thanks a bunch!

Answer by MathLover1(20849) (Show Source):
You can put this solution on YOUR website!
our matrix

Find the pivot in the 1st column in the 1st row

Make the pivot in the 2nd column by dividing the 2nd row by 2

Eliminate the 2nd column

Solution set:

- free
Therefore the solutions can be written as
(, , ) = (,,)

Because we want to find non-negative solutions, we have three inequalities

so,

and

so, the integer values of satisfying all of those inequalities ,, and are
=,,,,,,,,
so, there will be nine non-negative solutions

SOLUTION: For the following systems of equations in echelon form, tell how many solutions there are in nonnegative integers. x - 7y+4z = 75; 2y+7z=60. Thanks a bunch!