We have,

23x – 29y = 98 …(i)

29x – 23y = 110 …(ii)

To solve these equations, we need to simplify them.

So, by adding equations (i) and (ii), we get

(23x – 29y) + (29x – 23y) = 98 + 110

⇒ (23x + 29x) – (29y + 23y) = 208

⇒ 52x – 52y = 208

Now dividing it by 52, we get

x – y = 4 …(iii)

Similarly, subtracting equations (i) and(ii),

(23x – 29y) – (29x – 23y) = 98 – 110

⇒ (23x – 29x) – (29y – 23y) = - 12

⇒ - 6x – 6y = - 12

Dividing the equation by - 6, we get

x + y = 2 …(iv)

To solve equations (iii) and (iv), we need to make one of the variables (in both the equations) have same coefficient.

Here the variables x & y in both the equations have same coefficients.

⇒ 2x + 0 = 6

⇒ 2x = 6

⇒ x = 3

Substitute x = 3 in eq.(iii)/eq.(iv), as per convenience of solving.

Thus, substituting in eq.(iv), we get

3 + y = 2

⇒ y = - 1

Hence, we have x = 3 and y = - 1.