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# Find two numbers such that the sum of twice the first and thrice the second is 92, and four times the first exceeds seven times the second by 2.

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This is the Important question based on Linear Equations in two Variables Chapter of R.S Aggarwal book for
ICSE & CBSE Board.
In this Question you have to find the two numbers such that the sum of twice the first and thrice the second is
given, and four times the first exceeds seven times the second by given number.
This is the Question Number 5 Of Exercise 3E of RS Aggarwal Solution

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1. 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.

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