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Calculating base voltage of  NPN transistor 

I'm having trouble using the nodal equations to determine the base voltage Vb1 in the circuit below. I've attempted to write  seven equations below, but not able to fit them in entirely.

![Ltspice snapshot circuit](https://electrical.codidact.com/uploads/hzuifdmzx68devg67j8deqm7sy9h)

(12-Vx)/1.62k = (Vx-Vy)/1.21k +(Vx-Vb1)/1k----equation 1

(Vx-Vy)/1.21k = Vy/1.21k + (Vy-Vb2)/27k------ equation 2

(Vy-Vb2)/27k = Vb2/5.62k + Ib2-------- equation 3

(Vx-Vb1)/1k  = Vb1/1k + Ic2 + Ib1------ equation 4

Ib2= (Vb2-0.7) /(310 * beta 2)-------  equation 5

Ic2= (Vb2-0.7)/310 ------ equation 6

Ib1=(Vb1-0.7)/(200* beta 1) ------ equation 7

Is it possible to apply the Thévenin's at nodes Vx and Vy one by one ?

While applying Thévenin's at  Vx , How to deal with node Vy ?

Looking forward to suggestions / help on simplifying the circuit equations.