The problem is:

2x + 5y + 4z = 21

4x - 5y +z = 38

6x - z = 17

step by step please.

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- Jun 3rd 2009, 05:43 PMhelpmeGaussian Elimination
The problem is:

2x + 5y + 4z = 21

4x - 5y +z = 38

6x - z = 17

step by step please. - Jun 3rd 2009, 06:06 PMProve It
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.

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

$\displaystyle 26x + 5y = 87$

$\displaystyle 10x - 5y = 55$

$\displaystyle 6x - z = 17$

Now do $\displaystyle R_1: R_1 + R_2$

$\displaystyle 36x = 144$

$\displaystyle 10x - 5y = 55$

$\displaystyle 6x - z = 17$.

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

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

$\displaystyle 40 - 5y = 55$

$\displaystyle -5y = 15$

$\displaystyle y = -3$.

$\displaystyle 24 - z = 17$

$\displaystyle z = 7$.

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.