Can two states of an ideal gas be connected by an isothermal process as well as an adiabatic process?

An isothermal process is represented by

PV = constant … (i),

where P = pressure, V = volume.

This gives

P₁ V₁ = P₂ V₂ (ii),

Where

P₁, V₁ = initial values of pressure and volume

P₂, V₂ = final values of pressure and volume.

An adiabatic process is represented by

PV