## Solve the following system of equations for all three variables. -7x+y+z= −7x+y+z= \,\,-9 −9 -7x+5y-9z=

Question

Solve the following system of equations for all three variables.
-7x+y+z=
−7x+y+z=
\,\,-9
−9
-7x+5y-9z=
−7x+5y−9z=
\,\,-3
−3
7x-6y+4z=
7x−6y+4z=
\,\,-6
−6

in progress 0
3 weeks 2021-09-24T20:44:49+00:00 1 Answer 0

(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 =