Two species A and B are at VLE. Their saturated vapor pressures follow Antoine Equations:

Temperature $($T$)$ should stay in Celsius for all calculations

Pressure $($P$)$ should stay in kPA for all calculations

$\backslash$gamma does not equal y and are not the same variable

$ln(P_A^{\text{s}\text{a}\text{t}})=14\mathrm{.}3-\frac{2750}{T+228},ln(P_B^{\text{s}\text{a}\text{t}})=15\mathrm{.}4-\frac{3000}{T+200}$

The activity coefficients of species A and $B$ can be expressed as:

$ln{}_A=C{x}_B^2,ln{}_B=C{x}_A^2$ where $C=3\mathrm{.}00-0\mathrm{.}02T(inC)$

Find the equilibrium temperature and liquid phase composition of A and $B$ if $P=50$kPa and

$y_A=0\mathrm{.}6.$