Let $$x = \frac{{5\frac{3}{4} - \frac{3}{7} \times 15\frac{3}{4} + 2\frac{2}{{35}} \div 1\frac{{11}}{{25}}}}{{\frac{3}{4} \div 5\frac{1}{4} + 5\frac{3}{5} \div 3\frac{4}{{15}}}}.$$      When y is added to x, the result is $$\frac{7}{{13}}.$$ What is the value of y?

$$\eqalign{ & x = \frac{{5\frac{3}{4} - \frac{3}{7} \times 15\frac{3}{4} + 2\frac{2}{{35}} \div 1\frac{{11}}{{25}}}}{{\frac{3}{4} \div 5\frac{1}{4} + 5\frac{3}{5} \div 3\frac{4}{{15}}}} \cr & x = \frac{{\frac{{23}}{4} - \frac{3}{7} \times \frac{{63}}{4} + \frac{{72}}{{35}} \div \frac{{36}}{{25}}}}{{\frac{3}{4} \div \frac{{21}}{4} + \frac{{28}}{5} \div \frac{{49}}{{15}}}} \cr & x = \frac{{\frac{{23}}{4} - \frac{{27}}{4} + \frac{{10}}{7}}}{{\frac{1}{7} + \frac{{12}}{7}}} \cr & x = \frac{{ - \frac{4}{4} + \frac{{10}}{7}}}{{\frac{{13}}{7}}} \cr & x = \frac{{\frac{{ - 7 + 10}}{7}}}{{\frac{{13}}{7}}} \cr & x = \frac{3}{{13}} \cr & x + y = \frac{7}{{13}} \cr & y = \frac{7}{{13}} - \frac{3}{{13}} \cr & y = \frac{4}{{13}} \cr} $$