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2 years ago

Solve the following system of equations for all three variables.

Mathematics

1 answer:

GrogVix [38]2 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

-1y - 5z = - 9

-7x + y + z = -9

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

-7x + y + z = -9

7x - 5y + 9z = 3

-4y - 10z = -6

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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