Question

$$\begin{gathered} 41x-17y=99, \\ 17x-41y=75. \end{gathered}$$

Answer 1

The given equations are:
41x − 17y = 99 .............(i)
17x − 41y = 75 .............(ii)
On adding (i) and (ii), we get:
58x − 58y = 174
⇒ 58(x − y) = 174
⇒ x − y = 3 ............(iii)

On subtracting (ii) from (i), we get:
24x + 24y = 24
⇒ 24(x + y) = 24
⇒ x + y = 1 ...............(iv)

On adding (iii) and (iv), we get :
2x = 4 ⇒ x = 2

On substituting x = 2 in (iii), we get:
2 − y = 3
⇒ y = 2 − 3 = −1

Hence, the required solution is x = 2 and y = −1.