System of equations in 3 variables.

• December 2nd 2009, 04:38 PM
kelsikels
System of equations in 3 variables.
1.) 2x + 10y + 6z = 8
x + 5y + 3z = -2
x + y + z = -4

Help! Thanks.
• December 2nd 2009, 04:54 PM
Bacterius
First equation :

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

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

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

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

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

Becomes :

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

Which simplifies to $4 = -2$ (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 $-4 = 2$, there cannot exist any solutions ? Or is it better to use the discriminant ?
• December 2nd 2009, 04:56 PM
mathceleb
Quote:

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

Help! Thanks.