System of equations in 3 variables.

1.) 2x + 10y + 6z = 8
x + 5y + 3z = -2
x + y + z = -4


Help! Thanks.

First equation :



Can be written :

And may also be written :

Substitute the left-hand-side into the second equation :



Becomes :



Which simplifies to (Sweating)

There is something terribly wrong with your system, you are sure you didn't make an error while copying them on the forum ? (Wondering)

EDIT : ahah good working mathceleb, didn't think about the discriminant. By the way, is it correct to say that since his equation simplifies to , there cannot exist any solutions ? Or is it better to use the discriminant ?

Quote:

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Originally Posted by kelsikels

1.) 2x + 10y + 6z = 8
x + 5y + 3z = -2
x + y + z = -4


Help! Thanks.

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No solution exists to your system, because your discriminant = 0.


See here for the math behind my answer using Cramer's Rule:

3 unknown Cramer's Rule