# Math Help - Gaussian Elimination

1. ## Gaussian Elimination

The problem is:

2x + 5y + 4z = 21
4x - 5y +z = 38
6x - z = 17

2. Originally Posted by helpme
The problem is:

2x + 5y + 4z = 21
4x - 5y +z = 38
6x - z = 17

Usually I would say to eliminate the x values first, but in this case it looks easier to eliminate the z's.

Do the following.

$R2: R_2 + R_3$ and $R_1: R1 + 4R_3$

$26x + 5y = 87$
$10x - 5y = 55$
$6x - z = 17$

Now do $R_1: R_1 + R_2$

$36x = 144$
$10x - 5y = 55$
$6x - z = 17$.

Now you can solve for x. $x = 4$.

Substitute this value into the other two equations to solve for y and z.

$40 - 5y = 55$

$-5y = 15$

$y = -3$.

$24 - z = 17$

$z = 7$.

So your solution is [tex](x, y, z) = (4, -3, 7).

You could substitute these back into your original equation to check if you wish.