A great deal is learned in Halacha, from the words, ואכלת ושבעת וברכת, “You shall eat, be satiated, and bless.” The obvious reference here is that the reciting of Birkat Hamazon, Grace After Meals, is a Torah commandment.
It is derived from these words, situations where one can help another fulfill the Mitzva of making a blessing, simply by answering Amen to another person’s blessing.
This can be done, when the two individuals have an equal obligation to recite that Bracha. The Shulchan Aruch writes that because women have the same obligation to hear the Kiddush on Friday night, a woman can recite the Kiddush, and her husband fulfills his obligation by answering אמן. ( The Minhag is that women do not recite Kiddush for men, but, technically, they can.)
Women have the same obligation to hear the Megilla as other women. The obligation for men is slightly different, as there is a command for men to read it, as well. Therefore, women can read the Megilla for other women, but not for men.
There is a little known Halacha, that says that a boy, before the age of Bar Mitzva, can recite Birkat Hamazon for his father, who fulfills the Mitzva by way of his minor son.
This takes place only when the father has not eaten the required amount of food to be satiated. Like his son, his obligation to “Bench” is only rabbinical. His son is practicing for his adult obligation, which makes his Benching, rabbinical.
Since they both have equal rabbinic obligations, the son can be “מוציא”, have his father fulfill his obligation, by way of his son.
These, and many other Halachot, are learned from the words, ואכלת ושבעת וברכת.