# Thread: simultaneous equations, 3 unknowns

1. ## simultaneous equations, 3 unknowns

Hey, need some help with the methodology involved in solving simultaneous equations with three unknowns.

I1 = I2 + I3
8I1= 3I3
3I1+5I2=3.4

cheers.

2. Originally Posted by clayson
Hey, need some help with the methodology involved in solving simultaneous equations with three unknowns.

I1 = I2 + I3
8I1= 3I3
3I1+5I2=3.4

cheers.
First rearrange your second two equations to get them with respect to $\displaystyle I1$

$\displaystyle 8I1 = 3I3$, therefore $\displaystyle I3 = \frac{8}{3}I1$

For the second one, do the same:

$\displaystyle 3I1 + 5I2 = 3.4$, $\displaystyle 5I2 = 3.4 - 3I1$, so $\displaystyle I2 = \frac{3.4 - 3I1}{5}$.

Now put these values of $\displaystyle I2$ and $\displaystyle I3$ in to your first equation, you now have an equation in terms of just $\displaystyle I1$.

Solve this and then put your value for $\displaystyle I1$ back into the second and third equations to find all terms.