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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 by2.

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An important question from linear equations in two variables as it was already asked in previous year papers in which we have been asked to 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.

RS Aggarwal, Class 10, chapter 3E, question no 5

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### 1 Answer

1. Given :Â  two numbers are such that the sum of twice the first and thrice the second isÂ 92, and four times the first exceeds seven times the second byÂ 2.
To find : the two numbers
LetÂ xÂ andÂ yÂ be the two numbers required.
According to the question :
â‡’2x+3y=92Â  Â  Â  Â  Â  Â ……..(1)
â‡’4xâˆ’7y=2Â  Â  Â  Â  Â  Â  ……..(2)
multiply the first equation byÂ 2Â , and subtract eqnÂ (1)Â from eqnÂ (2)
4x+6y=184
âˆ’(4xâˆ’7y=2)Â , we get
â‡’13y=182
â‡’y=182â€‹/13=14
PutÂ y=14Â inÂ (1)
2x+3y=92
â‡’2x+3Ã—14=92
â‡’2x=92âˆ’42=50
âˆ´x=50/2â€‹=25
âˆ´x=25Â andÂ y=14

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