Why Do My Calculations with Kirchoff's Laws Seem Incorrect?

[ahben86]

I was hoping someone could help out, I am working out a problem with Kirchoff's Laws and cannot seem to get the math to work out properly, at least I think the math is not working properly.
I was hoping to run it by someone here.

Homework Statement

The circuit is as follows:
A battery of 24 V on one end connected to two parallel resistors with values of 5 Ω and 7 Ω.
Mesh one will be the loop between the battery and the 5 Ω resistor, which has a current of I₁.
Mesh two will be the loop between the 5 Ω resistor and the 7 Ω resistor, which has current of I₂.

Homework Equations

The equations I set up are as follows:
0 = -24 + 5*(I₁ - I₂)
0 = 7*I₂ + 5*(I₂ - I₁)

The Attempt at a Solution

After calculating the values I obtained these numbers:
I₁ = 8.229 A
I₂ = 3.429 A

I tried verifying these answers by using V = I*R
Finding R_eq to be 2.917 Ω.
Therefore I = V/R and I = 8.228 A and since the current from I₁ is the same value it seems that the values obtained from Kirchoff's Laws do not match the Ohm's Law current.

I am uncertain if I am not realizing a concept but this does not make sense to me.

Any help is appreciated.
Thank you,
A.B.

 

[Delphi51]

I think your work is all correct. V =IR finds the current through the resistors as 4.8 and 3.42 representing I1 - I2 and I2, so I2 = 3.42,
I1 - I2 = 4.8
I1 = I2 + 4.8
I1 = 3.42 + 4.8 = 8.23

 

[ahben86]

thank you for your help Delphi, sorry I posted in the wrong area.
I think I understand now,

A. B.

 

[Delphi51]

Most welcome! This is the correct area for your question.