Question

97x − 78y = 310, 78x − 97y = 215

Answer 1

Here,

97x − 78y = 310      ...(1)

78x − 97y = 215      ...(2)

Adding equation (1) and equation (2):

(97x − 78y) + (78x − 97y) = 310 + 215

97x − 78y + 78x − 97y = 525

97x + 78x − 78y − 97y = 525

175x − 175y = 525     ...(Dividing equation by 175)

x − y = 3     ...(i)

Subtracting equation (2) from equation (1):

(97x − 78y) − (78x − 97y) = 310 − 215

97x − 78y − 78x + 97y = 95

97x − 78x − 78y + 97y = 95

19x + 19y = 95     ...(Dividing equation by 19)

x + y = 5     ...(ii)

Now, let’s add equations (i) and (ii):

(x − y) + (x + y) = 3 + 5

2x = 8

x = `8/2`

∴ x = 4

Substituting x = 4 in equation (ii):

4 + y = 5

y = 5 − 4

∴ y = 1