# Gaussian Elimination

• Jun 3rd 2009, 05:43 PM
helpme
Gaussian Elimination
The problem is:

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

• Jun 3rd 2009, 06:06 PM
Prove It
Quote:

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.

\$\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.