Question

Solve for x and y:

23x – 29y = 98, 29x – 23y = 110

Answer 1

The given equations are:

23x – 29y = 98   ...(i)

29x – 23y = 110   ...(ii)

Adding (i) and (ii), we get:

52x – 52y = 208

⇒ x – y = 4   ...(iii)

Subtracting (i) from (ii), we get:

6x + 6y = 12

⇒ x + y = 2   ...(iv)

Now, adding equation (iii) and (iv), we get:

2x = 6

⇒ x = 3

On substituting x = 3 in (iv), we have:

3 + y = 2

⇒ y = 2 – 3

⇒ y = –1

Hence, x = 3 and y = –1.