Finding the Voltage across a Resistor using the Node Voltage Method

[rugerts]

Homework Statement

For the given circuit (see below), find the voltage across resistor 3.

Homework Equations

n-1 Kirchhoff's Current Laws for n nodes.

The Attempt at a Solution

Can anyone verify whether my KCL equations are correct? The mixture of source voltages with node voltages may have stumped me as far as finding a relevant expression for current across for example resistor 4.
My answer for V1, which is the same as the voltage across resistor 3, comes out to 134.59 V and the answer appears to be 84.54 V.
I have tried using Cramer's rule.

Here are imgur links incase the above images are too blurry:
https://imgur.com/KKL49X7
https://imgur.com/N79tdYo

 

[ehild]

Homework Statement

For the given circuit (see below), find the voltage across resistor 3.

Homework Equations

n-1 Kirchhoff's Current Laws for n nodes.

The Attempt at a Solution

View attachment 239069 View attachment 239070

Can anyone verify whether my KCL equations are correct? The mixture of source voltages with node voltages may have stumped me as far as finding a relevant expression for current across for example resistor 4.
My answer for V1, which is the same as the voltage across resistor 3, comes out to 134.59 V and the answer appears to be 84.54 V.
I have tried using Cramer's rule.

Here are imgur links incase the above images are too blurry:
https://imgur.com/KKL49X7
https://imgur.com/N79tdYo

Check the signs in your equations. Remember, the current flows from higher potential to lower one.
Also, it would be easier to write KCL equation for the nod at the ground instead of node 2.

 

[gleem]

The most efficient way would be to use the method of replacing the voltage sources with current sources and vice verse.