`2x + y - z = 7, x - 2y + 2z = -9, 3x - y + z = 5` Solve the system of linear equations and check any solutions algebraically.

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You may use the reduction method to solve the system, hence, you may multiply the first equation by 2, such that:

`2(2x + y - z) = 2*` 7

`4x + 2y - 2z = 14`

You may now add the equation `4x + 2y - 2z = 14 ` to the second equation ` ` `x` `- 2y + 2z = -` 9, such that:

`4x + 2y - 2z + x - 2y + 2z= 14 - 9`

`5x = 5 => x = 1`

You may replace 1 for x in equation `3x - y + z = 5` , such that:

`3 - y + z = 5 => -y + z = 2`

You may also replace 1 for x in equation `x - 2y + 2z = -9` , such that:

`1 - 2y + 2z = -9 => - 2y + 2z = -10 => y - z = 5`

You may add the equations `y - z = 5` and `-y + z = 2:`

`-y + z + y - z= 2 + 5 => 0 = 7` inaccurate.

Hence, evaluating the solution to the given system, yields that there are no solutions.

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