# Linear Equation 24

### From Homeworkwiki

**Solve : 65 x - 33 y = 97 and 33 x - 65 y = 1**

**Solution :**

In this problem, the coefficient of x in the first equation is numerically equal to the

coefficient of y in second equation and the coefficient of y in the first equation is numerically

equal to the coefficient of x in the second equation.

Such equations are solved by the method as given below:

65 x - 33 y = 97 -------------------------------- (i)

and, 33 x - 65 y = 1 ---------------------------- (ii)

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

98 x - 98 y = 98

=> x - y = 1 ----------------------------------- (iii) [dividing each term by 98]

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

32 x + 32 y = 96

=> x + y = 3 ----------------------------------- (iv) [dividing each term by 32]

Now on solving equations (iii) and (iv), we get

**x = 2 and y = 1**