solve this equation using gaussian or gauss-jordan elimination 4x+8y-z=10 3x-8y+9z=14 7x+6y+5z=0

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You need to use gaussian elimination, hence, you need to convert the original form of the system to a triangular form.

You need to eliminate the variable x from the first and second equations and then, from the first and the third equations such that:

`{(4x+8y-z=10|*(-3)), (3x-8y+9z=14|*4):}` `=gt{(-12x-24y+3z=-30),(12x-32y+36z=56):}`

Adding the equations yields:

`-56y + 39z = 26`

Considering the first and the third equations yields:

`{(4x+8y-z=10|*(7)), (7x+6y+5z=0|*(-4)):}` `=>{(28x+56y-7z=70),(-28x-24y-20z=0):}`

Adding the equations yields:

`32y - 27z = 70`

You need to use the equations -`56y + 39z = 26`  and `32y - 27z = 70`  to eliminate y such that:

`{(-56y + 39z = 26|*4),(32y - 27z = 70|*7):}=gt` `{(-224y + 156z = 104),(224y - 189z = 490):}`

`-33z = 594 => z = -18`

Substituting -18 for z in equation `32y - 27z =...

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