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Question

If 29x+37y=103 and 37x+29y=95 then
(a) x = 1, y = 2 (b) x = 2, y = 1 (c) x = 3, y = 2 (d) x = 2, y = 3

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Solution

The given equations are
29x+37y=103 .....i37x+29y=95 .....ii
Adding (i) and (ii), we get
66x+66y=198x+y=3 .....iii
Subtracting (i) from (ii), we get
8x-8y=-8x-y=-1 .....iv
Adding (iii) and (iv), we get
2x=2x=1
Substituting x = 1 in (iii), we have
1+y=3y=2
Thus, x = 1 and y = 2.
Hence, the correct answer is option (a).

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