Solve: 23x + 29y = 98, 29x + 23y = 110.

1.	Solve: 23x + 29y = 98, 29x + 23y = 110.
Answer» The given equations are as follows: 23x + 29y = 98 ………….(i) 29x + 23y = 110 …………(ii) On adding (i) and (ii), we get: 52x + 52y = 208 ⇒ x + y = 4 …………(iii) On subtracting (i) from (ii), we get: 6x – 6y = 12 ⇒ x – y = 2 …………(iv) On adding (iii) and (iv), we get: 2x = 6 ⇒ x = 3 On substituting x = 3 in (iii), we get: 3 + y = 4 ⇒ y = 4 – 3 = 1 Hence, the required solution is x = 3 and y = 1.

Answer»

The given equations are as follows:

23x + 29y = 98 ………….(i)

29x + 23y = 110 …………(ii)

On adding (i) and (ii), we get:

52x + 52y = 208

⇒ x + y = 4 …………(iii)

On subtracting (i) from (ii), we get:

6x – 6y = 12

⇒ x – y = 2 …………(iv)

On adding (iii) and (iv), we get:

2x = 6

⇒ x = 3

On substituting x = 3 in (iii), we get:

3 + y = 4

⇒ y = 4 – 3 = 1

Hence, the required solution is x = 3 and y = 1.

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