# How do you solve the system #x-y-z=2#, #2x+y+z=8#, and #x+y+z=6#?

##### 1 Answer

This set of equations can not be solved.

#### Explanation:

Given

[1]

[2]

[3]

Note that adding equations [1] and [2] together, we get

But adding equations [1] and [3] together, gives us

Since

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Since this was asked under "Solving a System of Equations Using a Matrix"

if you need the matrix version of this, here it is (using Gaussian elimination)

Augmented matrix:

The value in the pivot position for

has become