Solving nodal equations to find node voltages

[naivy]

Homework Statement

Homework Equations

V=IR, Nodal Analysis

The Attempt at a Solution

1 and 2 in the diagram are the nodal equations. Considering that the left node is V₁ and that the right node is V₂. I don't know how to get from the nodal equations to step 3. I know that you go from step 3 to step 4 using V=IR.

I tried solving the nodal equations to get to step 3...

Can someone please work it out for me? Thank you

Please help

 

[gneill]

In (2) replace I_x with V₁/10K. Solve for an expression for V₁. Substitute this expression for V₁ into (1). Solve for V₂. All done.

 

[naivy]

In (2) replace I_x with V₁/10K. Solve for an expression for V₁. Substitute this expression for V₁ into (1). Solve for V₂. All done.

Ohh wow. Now I feel dumb(er, as many would argue here at pf)...

Thanks for the help gneill!