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
Given : two numbers are 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.
To find : the two numbers
Let x and y be the two numbers required.
According to the question :
⇒2x+3y=92 ……..(1)
⇒4x−7y=2 ……..(2)
multiply the first equation by 2 , and subtract eqn (1) from eqn (2)
4x+6y=184
−(4x−7y=2) , we get
⇒13y=182
⇒y=182/13=14
Put y=14 in (1)
2x+3y=92
⇒2x+3×14=92
⇒2x=92−42=50
∴x=50/2=25
∴x=25 and y=14