Given :-
The sum of twice the first and thrice the second is 92, and four times the first exceeds seven times the second by 2.
To Find :-
The Numbers
Solution :-
Let the first number be x and the second number be y.
According to the Question
1st Equation
2x + 3y = 92 ……….(i)
2nd Equation
4x – 7y = 2 ………(ii)
On multiplying (i) by 7 and (ii) by 3,
14x + 21y = 644 ………..(iii)
12x – 21y = 6 ………..(iv)
On adding (iii) and (iv), we get
⇒ 26x = 650
⇒ x = 650/26
⇒ x = 25
Putting the x values Eq in (i)
⇒ 2x + 3y = 92
⇒ 2 × 25 + 3y = 92
⇒ 50 + 3y = 92
⇒ 3y = (92 – 50)
⇒ 3y = 42
⇒ y = 42/3
⇒ y = 14
Hence, the first number is 25 and the second number is 14.