3.) Solve the following system of equations for all three variables.
10x - y - 9z = 4
- 4x + y + 4z = -1
-X – y +z = 6

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  (x, y, z) = (8, -5, 9)

Step-by-step explanation:

A suitable calculator or app can solve linear systems larger than 2 equations in 2 unknowns. The attachment shows the solution to be ...

  (x, y, z) = (8, -5, 9)

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The third equation is conveniently solved for z, which can then be substituted into the other two equations to get two equations in two variables. These can be solved in any of the usual ways.

  z = 6 +x + y

The first equation becomes ...

  10x -y -9(6 +x +y) = 4   ⇒   x -10y = 58

  -4x +y +4(6 +x +y) = -1   ⇒   5y = -25

The latter gives you y = -5. Putting that in the former gives x = 8. Then the value of z is ...

  z = 6 +(8) +(-6) = 9

So, the solution is (x, y, z) = (8, -5, 9).

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