Question

The sum of four times the first number and three times the second number is 15. The difference of three times the first number and twice the second number is 7. Find the numbers.

Answer 1

Let the two numbers be x and y respectively.
Then, we have
4x + 3y = 15    ....(i)
3x - 2y = 7      ....(ii)
Multiplying eqn. (i) by 2 and eqn. (ii) by 3, we get
8x + 6y = 30  ....(iii)
9x - 6y = 21   ....(iv)
Adding eqns. (iii) and (iv), we get
17x = 51
⇒ x = 3
⇒ 4(3) + 3y = 15
⇒ 12 + 3y = 15
⇒ 3y = 3
⇒ y = 1
Thus, the two numbers are 3 and 1 respectively.