# set of linear simultaneous equations

• Jan 5th 2006, 08:01 PM
drown
Algebra Homework Help URGENT!!!
I have a huge algebra problem, that i need solved for me, and show me how it's done, if possible. Urgent reply needed its due very soon.

8k - 5n = 8r
3u + 2o = 189
5d + 2c = 6m
5L + 4m = 23b
3r - m = 3u
3k - 4i = 2i
3n - 3o = c
o - c = 4d
8i + 9r = 9n
10m + 7d = 3n
4d + 4e = 6b
4y - 6u = 2m
6b + 3c = 14m

L + e + n + n + y + c + o + n + u + n + d + r + u + m = ???
• Jan 5th 2006, 08:07 PM
drown
Well its sort of a riddle thing, i don't know, but could anyone help?
• Jan 5th 2006, 10:15 PM
CaptainBlack
Quote:

Originally Posted by drown
I have a huge algebra problem, that i need solved for me, and show me how it's done, if possible. Urgent reply needed its due very soon.

8k - 5n = 8r
3u + 2o = 189
5d + 2c = 6m
5L + 4m = 23b
3r - m = 3u
3k - 4i = 2i
3n - 3o = c
o - c = 4d
8i + 9r = 9n
10m + 7d = 3n
4d + 4e = 6b
4y - 6u = 2m
6b + 3c = 14m

L + e + n + n + y + c + o + n + u + n + d + r + u + m = ???

This is a set of linear simultaneous equations.

Reorganise them so that the variables and their coefficients appear on
the left hand side of each equation, and space them so that the terms
in a given variable all appear in the same column.

Then use Gaussian elimination to solve. An explanation of Gaussian elimination
together with a worked example may be found at:

http://mathforum.org/library/drmath/view/53207.html

RonL
• Jan 5th 2006, 10:33 PM
drown
Could you show me the answer? It would be a lot easier to figure out if i knew what it was.
• Jan 6th 2006, 01:58 AM
CaptainBlack
Quote:

Originally Posted by drown
Could you show me the answer? It would be a lot easier to figure out if i knew what it was.

Here is DrMath's example:
Quote:

Example:

-4*w + 3*x - 4*y - z = -37
-2*w - 5*y + 3*z = -20
-w - x - 3*y - 4*z = -27
-3*w + 2*x + 4*y - z = 7

Let w be the first pivot variable, and the first equation the first
pivot equation. w appears in the second equation, so we subtract
(-2)/(-4) = 1/2 times the first equation from the second, getting

-2*w - 5*y + 3*z = -20,
-2*w + (3/2)*x - 2*y - (1/2)*z = -37/2
--------------------------------------
-(3/2)*x - 3*y + (7/2)*z = -3/2

w appears in the third equation so we subtract (-1)/(-4) times the
first equation from the third. w appears in the fourth equation, so we
subtract (-3)/(-4) times the first equation from the fourth. This
leaves

-4*w + 3*x - 4*y - z = -37
-(3/2)*x - 3*y + (7/2)*z = -3/2
-(7/4)*x - 2*y - (15/4)*z = -71/4
-(1/4)*x + 7*y - (1/4)*z = 139/4

Now the last three equations are a system of three equations in three
unknowns, and we treat that similarly. Let x be the next pivot
variable, and the second equation the pivot equation. Since x appears
in the third equation, we subtract (-7/4)/(-3/2) = 7/6 times the
second equation from the third. Since x appears in the fourth equation
we subtract (-1/4)/(-3/2) = 1/6 times the second equation from the
fourth. This leaves

-4*w + 3*x - 4*y - z = -37
-(3/2)*x - 3*y + (7/2)*z = -3/2
(3/2)*y - (47/6)*z = -16
(15/2)*y - 16*z = 35

Now the last two equations are a system of two equations in two
unknowns, and we treat that similarly. Let y be the next pivot
variable, and the third equation the next pivot equation. Since y
appears in the fourth equation, we subtract (15/2)/(3/2) = 5 times the
third equation from the fourth. This leaves

-4*w + 3*x - 4*y - z = -37
-(3/2)*x - 3*y + (7/2)*z = -3/2
(3/2)*y - (47/6)*z = -16
(115/3)*z = 115

This completes the first phase.

Now we start with the last equation, and solve for z. This gives
z = 3, and we substitute that into the preceding equations:

-4*w + 3*x - 4*y = -34
-(3/2)*x - 3*y = -12
(3/2)*y = 15/2

The last remaining equation tells us that y = 5, and we substitute
that into the preceding equations:

-4*w + 3*x = -14
-(3/2)*x = 3

The last remaining equation tells us that x = -2, and we substitute
that into the preceding equation:

-4*w = -8

That gives us the value w = 2, and so the solution is

(w,x,y,z) = (2,-2,5,3)

Understood?
and the answer in this case is:

b=20, c=30, d=6, e=24, i=36, k=72, l=80, m=15, n=64, o=54, r=32, u=27, y=48.

I will not reproduce the actual manipulations here as they are a bit
long and would be too much typing.

RonL