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# Help. ​

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Help. Oct 23, 2017

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3x + 2y +  z  = 7     (1)

5x + 5y + 4z  = 3    (2)

3x + 2y + 3z  = 1    (3)

The object, NSS, is to eliminate a variable and end up with 2 equations with two unknowns

We can choose any variable that we want......here....z seems easiest

Multiply the first equation by -4  and add it to equation 2

-12x - 8y -  4z = -28

5x  + 5y + 4z =   3

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-7x - 3y          =  -25         →  7x + 3y = 25      (4)

Multiply the first equation by -3 and add it to to the 3rd equation

-9x - 6y - 3z = -21

3x  + 2y + 3z = 1

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- 6x - 4y      =  -20     →  6x + 4y  =  20    (5)

Multiply (4) by  4   and (5) by  -3

28x +12 y = 100

-18x -  12y  =  -60         add these together

10x =  40      divide both sides by 10

x = 4

Using (5) to find y, we have

6(4) + 4y = 20

24 + 4y  = 20    subtract24 from both sides

4y  = -4      divide both sides by 4

y = - 1

And using   3x  + 2y + 3z = 1  to find z, we have

3 (4) + 2 (-1) + 3z  = 1

12 - 2 + 3z  = 1

10 + 3z  = 1    subtract 10 from both sides

3z = -9       divide both sides by

z = -3

So....{ x , y, z }  =  { 4, -1, -3 }   Oct 23, 2017