# Thread: Solution for equations in the form 0 = ax + byz - cz

1. ## Solution for equations in the form 0 = ax + byz - cz

I am new to this forum and my math is a little rusty at this point, any help you guys could offer will be very much appriciated.

I have three or more equations in the form 0 = ax + byz - cz where a, b and c are known and would like to solve for x, y and z.

Cheers.

2. Originally Posted by DanDan7
I am new to this forum and my math is a little rusty at this point, any help you guys could offer will be very much appriciated.

I have three or more equations in the form 0 = ax + byz - cz where a, b and c are known and would like to solve for x, y and z.

Cheers.
have a look at a lesson ...

YouTube - Solving a Systems of Equations in three variables 3

3. Method of elimination/substitution does not work in this case.

Here are the 3 eqns
(1) 0 = 231x + 9.8yz - 0.3z
(2) 0 = 106x + 9.8yz - 0.19z
(3) 0 = 34x + 9.8yz - 0.13z

eqn (1) - (2) =
0 = 125x - 0.11z

eqn (2) - (3) =
0 = 72x - 0.06z

eliminating x from above eqns
z = 0

substituting z = 0
x = 0

substituting x= 0 and z = 0 into eqn 1
y = 0

however the result (0,0,0) is not the one I am looking for? Is there another method that you may suggest? Thanks.

4. Update:

Through manual iterations I have found the solution that I am looking for to be (0.85, 0.0106, 1000). However, I need need to create a C program that can solve these equations in the future, and so I need a method that is more appropriate than manual iterations. Any suggestions would be great.

Cheers.

5. Originally Posted by DanDan7
Through manual iterations I have found the solution that I am looking for to be (0.85, 0.0106, 1000).
(1) 0 = 231x + 9.8yz - 0.3z
(2) 0 = 106x + 9.8yz - 0.19z
(3) 0 = 34x + 9.8yz - 0.13z
(1) .23 = 231x + 9.8yz - 0.3z
(2) 3.98 = 106x + 9.8yz - 0.19z
(3) 2.78 = 34x + 9.8yz - 0.13z

(0,0,0) is the ONLY using your 3 equations; is there a typo anywhere?

6. Thanks for the reply. In my spreadsheet the values are to many decimal places, whereas the values provided on this post have been rounded. On the speadsheet, with more decimal places for greater accuracy all results are very close to zero.

Is there a generic name for an equation in the form 0 = ax + byz - cz ? I have so far been unable to find this eqn form elsewhere.

7. Originally Posted by DanDan7
Thanks for the reply. In my spreadsheet the values are to many decimal places, whereas the values provided on this post have been rounded. On the speadsheet, with more decimal places for greater accuracy all results are very close to zero.
Is there a generic name for an equation in the form 0 = ax + byz - cz ? I have so far been unable to find this eqn form elsewhere.
"Very close to zero" just ain't good nuff!

(1) 0 = 231x + 9.8yz - 0.3z
(2) 0 = 106x + 9.8yz - 0.19z
(3) 0 = 34x + 9.8yz - 0.13z

(1)(2): 231x - .30z = 106x - .19z
125x = .11z
z = 125x / .11 ***

(1)(3): 231x - .30z = 34x - .13z
197x = .17z
z = 197x / .17 ***

*** 125x / .11 = 197x / .17
21.67x = 21.25x
Get my drift?

Btw, with equations like:
(3) 0 = 34x + 9.8yz - 0.13z
I find it easier if I get rid of decimals:
(3) 0 = 3400x + 980yz - 13z