solve 23x + 35y = 209 , 35x + 23y = 197

23x + 35y = 209  ………………(1)

35x + 23y = 197   ………………(2)

Adding eqn 1and 2

We get,

58x + 58y = 406

58( x + y) = 406

x + y = 406/58

x + y = 7   -------------- (3)

now,

23x + 35y = 209

35x + 23y = 197

On subtraction, we get

-12x + 12y = 12

12 ( -x + y) = 12

-x + y = 12/12

-x + y = 1  ------------ (4)

Now taking (3) and (4)

 x + y = 7   

-x + y = 1

Adding these , we get

2y = 8

Y = 8/2

Y = 4

Put the value of y in eqn (3)

X + 4 = 7

X = 7 – 4

x = 3

 x = 3 and y = 4.