Question

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

Answer 1

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.