# Solve -6x-6y-2x=14 -6x+6y-4z=22 -5-y+3z=-7

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should eliminate one variable, hence, you need to add the first and the second equations to eliminate y such that:

`-6x - 6y - 2z - 6x + 6y - 4z = 14 + 22`

`-12x - 6z = 36`

Dividing by -6 yields:

`2x + z = -6`

You need to multiplicate the third equation by 6 such that:

`6(-5x-y+3z)=6*(-7) => -30x - 6y + 18z = -42`

You need to add the third equation, multiplied by 6, to the second equation, such that:

`-30x - 6y + 18z- 6x + 6y - 4z = -42 + 22`

`-36x + 14z = -20 => -18x + 7z = -10`

You need to multiplicate the equation `2x + z = -6`  by -7 such that:

`-14x - 7z = 42`

You need to add this equation to the equation  `-18x + 7z = -10`  such that:

`-14x - 7z - 18x + 7z= 42 - 10`

`-32x = 32 => x = -1`

You need to substitute -1 for x in equation `2x + z = -6`  such that:

`-2 + z = -6 => z = -4`

You need to substitute -1 for x and -4 for z in any of the three equations of the system such that:

`6 + 6y + 16= 22 => 6y = 22 - 22 => 6y = 0 => y = 0`

Hence, evaluating the solution to the system of equations yields `x = -1, y = 0 , z = -4` .