Consider a binary mixture for which the excess Gibbs energy is given by G^E/RT = 2.1x₁x₂ (x₁ + 2x₂). For each of the following overall compositions, determine whether one or two liquid phases will be present. If two liquid phases will be present, find their compositions and the amount of each phase present (phase fractions).

(a) z₁ = 0.2

(b) z₁ = 0.3

(c) z₁ = 0.5

(d) z₁ = 0.7

(e) z₁ = 0.8