1.) 2x + 10y + 6z = 8
x + 5y + 3z = -2
x + y + z = -4
Help! Thanks.
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 $\displaystyle 4 = -2$
There is something terribly wrong with your system, you are sure you didn't make an error while copying them on the forum ?
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 ?
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