# How do you solve using gaussian elimination or gauss-jordan elimination, 2x+4y-6z=48, x+2y+3z=-6, 3x-4y+4z=-23?

Jan 15, 2016

See Gaussian elimination for a very good explanation

$x = 3$, $y = 3$ and $z = - 5$

#### Explanation:

$2 x + 4 y - 6 z = 48$
$x + 2 y + 3 z = - 6$
$3 x - 4 y + 4 z = - 23$

Adding the first and third equations gives $5 x - 2 z = 25$
Doubling the second equation and adding it to the third gives $5 x + 10 z = - 35$
We can now use these two equations to solve for $z$ subtracting one from the other gives $- 12 z = 60$
$\therefore z = - 5$

$\therefore 5 x - 2 \left(- 5\right) = 25$
$5 x = 15$
$x = 3$

Returning to the original second equation:
$3 + 2 y + 3 \left(- 5\right) = - 6$
$2 y = - 6 - 3 + 15$
$y = 3$