The 5-card majors system was designed to quickly reveal a 4-4 trump fit or a 5-3 trump fit, where the 5-card suit is held by the Opener.

But when its the Responder who holds the 5-card suit the situation is not always immediately clear.
(Opener's bids are underlined)

1. After Opener's 1♠ a 2♥ reply by Responder clearly shows a . . . -card Hearts suit
   
   
2. Likewise in the sequence 1♣ - 1♠ - 1NT - 2♦   Responder shows . . . Spades, because he . . . . . . bid his Spades suit . . . . . . . . . , but skipped the . . . . . suit with his first bid.
   
   
3. And after an . . . . . by an Opponent of [1♥] a 1♠ bid by Responder also reveals a . . . . . . major suit, as with a . . . . . . suit he would have . . . . . . instead.
   
   
4. With a weak hand of . . . . points Responder has only few options and often his only choice is to rebid his . . . -card suit.
   (With 11+ pts hands Responder should not rebid . . . . . . . . . . , but jump rebid his . . . -card suit.)

It looks very similar to case "b" above, but it is not. Here Responder did bid his two suits . . . . . . . . , for he could not have bid his Clubs at the . . . level.   It is therefore not clear whether Responder holds 5 (or more) Spades or only 4.
To solve this riddle you must understand and follow the principle of . . . . . . . . . . .

Say you hold the following hand :

You opened and the bidding which went like this :   1♦ - 1♥ - 1NT - 2♣ -   what now ?

The answer is simple : by bidding . . . . . after Responder's 1♥ bid, you denied . . . . . . . . . . . . . . in his Hearts suit. Therefore when you support him on the second timer around he will know that you hold not . . . . . but . . . . . . cards in his suit.   This is the fundamental principle of . . . . . . . . . . . . . .

You of course still don't really know whether Partner actually holds . . . Hearts of . . . . .
But that does not matter, because your Partner will now know the exact card holding of the Hearts suit in the . . . . . . . . hands.

1. If that total is 8 he will . . . . . . . . . . . . . . . . . . (depending on his strength).
   
   
2. If on the other hand the combined card holding is only 7 Hearts, he will bid . . . . . . . . . , most likely . . . . . . .

When Responder holds a weak response hand of . . . . . points his rebid choices are limited. With no other options he will rebid his . . . -card suit, solving Opener's dilemma.

With all 11+ points hands Responders should at all cost avoid . . . . . . . . . . . It is not necessary, as it is Opener's r . . . . . . . . to give delayed support when he holds . . . -card support. But Responder may . . . . . . his . . . -card suit.

In all other cases where Responder holds a 5-card major, he should find a second bid in . . . . . suit or bid 2 . . . , to give Opener the opportunity to show . . . . . . . . . . . . .

Example 1

Responder ♠ - 9 ♥ - A Q 8 5 3 ♦ - 10 9 4 ♣ - K Q 9 6

Bidding : (N) 1♦ - 1♥ - 1NT - 2♣ - ? Comment : If Opener shows delayed support for your Hearts, raise to 4♥. If Opener rebids 2NT, bid 3♦! This will alert him to the fact you are . . . . . in . . . . ., likely with . . . . . , . Depending on Opener's Spade stoppers he may bid 3 or 4♥, preferring trump contract with a 2-5 holding over a dicey 3NT.

Example 2

Responder ♠ - K Q 10 9 4 ♥ - 8 3 ♦ - J 10 4 ♣ - K Q 9

Bidding : (N) 1♦ - 1♠ - 1NT - 2♣ - ? Comment : Opener is unlikely to raise your Clubs, so bidding it as a . . . . . . (containing only . . . cards) and showing your . . . . is a good option. It provides Opener with an opportunity to show . . . . . . . Raise Opener's 2♠ to 3, or his 2NT to 3NT.

Bidding a false suit is the bid of a . . . . . with only . . . . . . in that suit. You make such a bid

1. to show a . . . . . . . for a possible NO Trump contract
   
   
2. to give your Partner another bidding opportunity to show . . . . . . . . (for your . . . -card suit)
   
   
3. or you hold . . . . . points and can not immediately raise Partner's suit (for which you do have . . . . . . ) as a first bid.

Example 3

Responder ♠ - K Q 9 ♥ - A K 10 9 4 ♦ - 7 4 ♣ - 9 8 4

Bidding : (N) 1♦ - 1♥ - 1NT - 2♠ - ? Comment : Opener can not . . . . . . . . . . . For by responding with 1NT after your Heart bid he has denied . . . . . . . . . You can therefore safely bid your . . . . . Spade suit, showing you hold . . . . . . . . there.   Raise Opener's 3♥ to 4, or his 2NT to 3NT.

Note : You did not show a . . . . -card Hearts suit in above example, because you could have been bidding your 4-card suits naturally . . . . . . . . !
Also your Spade bid alerts Partner to the fact that you don't hold a . . . . . . stopper (if you had both . . . . and . . . . stoppers you would have rebid. . . . . instead of 2♠), in case he is looking for 3NT.

The Law of Total Tricks, as defined by the French Bridge theorist Jean-Rene Vernes says :

For example if your side has (5 + 3 =) 8 Spades and the Opponents possess (5 + 4 =) 9 Diamonds, the total number of tricks that can be made with contracts in these two suits is . . . . . . . . . tricks.

The actual tricks makable need not be divided . . . . . , as they depend on the . . . . . . . or . . . . . . . . location of . . . . . . . cards like . . . . . or a . . . . . For example if a . . . . sits . . . . . the Ace it will likely . . . . . . , but if it sits . . . . . . . the Ace it will probably . . . . . .. . . . . .

Nevertheless, it is a good rule of thumb (when competing for a Part score) to bit up to the . . . . level with . . . . trumps and up to the . . . . . level with . . . trumps. Or, when . . . . . . . . . . you might bid up to the . . . . . level with just 8 trumps, happy to . . . . . . . . . . .

The Law of Total Tricks is most useful when competing for a Part score (= a contract below a Game contract) against the Opposition. So the vital question arises : "How many trumps do we have in the combined hands?"

This is where the so-called Support Double comes into the picture.

The Opener
The Opener can make a . . . . . . . . . . . after Responder's . . . . . . suit has been overcalled :

The Support Double in above scenario in fact replaces the . . . . . . . . . . . . bid, the Opener otherwise would have made one bid later. So the Opponent's Overcall provides the opportunity for the Opener to show his . . . . . . . -card support straight away.

The Responder may of course have bid only a . . . . . -card suit anyway, but in that case Responder will either . . . . . . Opponent's . . . . . , or bid another . . . . . or . . . . . (with an . . . . . . . . . stopper).