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xxMikexx [17]
3 years ago
5

Solve the following system of equations for all three variables.

Mathematics
1 answer:
GrogVix [38]3 years ago
4 0

Answer:

(x,y,z) -> (2,4,1)

Step-by-step explanation:

-7x + y + z = -9

-7x + 5y - 9z = -3

7x - 6y + 4z = -6

Pick two pairs:

-7x + 5y - 9z = -3

7x - 6y + 4z = -6

and

-7x + y + z = -9

-7x + 5y - 9z = -3

Eliminate the same variable from each system:

-7x + 5y - 9z = -3

7x - 6y + 4z = -6

+ 5y - 9z = -3

- 6y + 4z = -6

<u><em>-1y - 5z = - 9</em></u>

-7x + y + z = -9

-7x + 5y - 9z = -3

-7x + y + z = -9

7x - 5y + 9z = 3

<u><em>-4y - 10z = -6</em></u>

Solve the system of the two new equations:

-1y - 5z = - 9           ->      -4 ( -1y - 5z = - 9)     ->   4y + 20z = 36  

-4y - 10z = -6          ->           -4y - 10z = -6      ->   -4y - 10z = -6

10z = 30

Thus, z = 3

-4y - 10z = -6

-4y - 10(3) = -6

-4y - 30 = -6

-4y = 24

Thus, y = -6

Substitute into one of the original equations:

-7x + y + z = -9

-7x + (-6) + (3) = -9

7x + -3  = -9

7x  = -6

x =

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