Solution:
$$\eqalign{
& 7x + 11y = 3\,\,\,\,*1 \cr
& \underline {\,8x + y = 15\,} \,\,\,\,\,\underline {\,*11\,} \cr
& \,\,7x + 11y = 3 \cr
& \,\,88x + 11y = 165 \cr
& \underline {\, - \,\,\,\,\,\,\,\,\, - \,\,\,\,\,\,\,\,\,\, - \,\,\,\,\,\,\,\,\,\,} \cr
& - 81x = - 162 \cr
& x = 2 \cr
& y = 15 - 8 \times 2 \cr
& y = - 1 \cr} $$
Put value of x and y in options only option 'D' satisfy in this values
3x + 5y = 1
3 × 2 + 5 × (-1) = 1
6 - 5 = 1 = 1 [satisfied]