2 audio cassettes and 3 video cassettes cost Rs. 425 and 3 audio cassettes and2 video cassettes cost Rs. 350. What are the prices of an audio cassetteand of a video cassette?

Let the price of an audio cassette be Rs. x and of a video
cassette be Rs. y.
Case 1:
2 audio cassettes and 3 video cassettes cost Rs. 425.
2x + 3y = 425 … (1)
Case 2:
3 audio cassettes and 2 video cassettes cost  Rs. 350
3x + 2y = 350 … (2)
Multiplying (1) by 2 and (2) by 3, we get
2 (2x + 3y = 425)
4x + 6y = 850 … (3)
3 (3x + 2y = 350)
9x + 6y = 1050  … (4)
Subtracting (4) from (3)
4x + 6y = 850
9x + 6y = 1050
(-)   (-)    (-)
------------------
-5x       = -200
⇒ x = 200/5

∴ x = 40
Substituting x = 40 in (1)
⇒ 2 (40) + 3y = 425
⇒ 80 + 3y = 425
⇒ 3y = 425 - 80
⇒ 3y = 345
⇒ y = 345/3
∴ y = 115
Ans.The price of an audio cassette is Rs. 40 and the price of a video cassette is Rs. 115.

Verification:
(a) 2x + 3y = 2 (40) + 3 (115) = 80 + 345 = 425
(b) 3x + 2y = 3 (40) + 2 (115) = 120 + 230 = 350.