1.) 2x + 10y + 6z = 8

x + 5y + 3z = -2

x + y + z = -4

Help! Thanks.

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- Dec 2nd 2009, 03:38 PMkelsikelsSystem of equations in 3 variables.
1.) 2x + 10y + 6z = 8

x + 5y + 3z = -2

x + y + z = -4

Help! Thanks. - Dec 2nd 2009, 03:54 PMBacterius
First equation :

$\displaystyle 2x + 10y + 6z = 8$

Can be written : $\displaystyle 10y + 6z = 8 - 2x$

And may also be written : $\displaystyle 5y + 3z = 4 - x$

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

$\displaystyle x + 5y + 3z = -2$

Becomes :

$\displaystyle x + (4 - x) = -2$

Which simplifies to $\displaystyle 4 = -2$ (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 $\displaystyle -4 = 2$, there cannot exist any solutions ? Or is it better to use the discriminant ? - Dec 2nd 2009, 03:56 PMmathceleb
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