You're missing some of the key equations related to the BJT, try combining these:

Equations for each Vcc to GND branches:

Vcc - I1R1 - I2R2 - Ib = 0 (account for I1 splitting off into base current and I2)

Vcc - IcR3 - Vce - R4Ie = 0

Equation for Base Emitter Loop:

I2R2 - Vbe = R4I4

(Usually assume Vbe ~ 0.6V): I2R2 - R4I4 = 0.6V

Equations relating Ic, Ie, and Ib:

Ie = Ic + Ib

Ib = beta*Ic

NOTE: Take particular note of the second and last equation I have listed, which are key to solving this type of problem

You're missing some of the key equations related to the BJT, try combining these:

Equations for each Vcc to GND branches:

Vcc - I1R1 - I2R2 - Ib = 0 (account for I1 splitting off into base current and I2)

Vcc - IcR3 - Vce - R4Ie = 0

Equation for Base Emitter Loop:

I2R2 - Vbe = R4I4

(Usually assume Vbe ~ 0.6V): I2R2 - R4I4 = 0.6V

Equations relating Ic, Ie, and Ib:

Ie = Ic + Ib

Ib = beta*Ic

NOTE: Take particular note of the second to last and last equation I have listed, which are key to solving this type of problem