`2x + y - 3z = 4, 4x + 2z = 10, -2x + 3y - 13z = -8` Solve the system of linear equations and check any solutions algebraically.

You may add the third equation to the first, such that:

`4y  - 16z = -4 => y - 4z = -1`

You may add the second equation to the third, multiplied by 2, such that:

`4x + 2z - 4x + 6y - 26z = 10 - 16`

`  -24z + 6y = -6 => -4z + y = -1`

Since you have obtained two equivalent equations, hence, the lines represented by the equations of the system are parallel and the system has no solutions.