Solve the following pair of equations - : 47x + 31y = 63 and 31x + 47y = 15.

47x + 31y = 63 ……(1)

31x + 47y = 15 ……(2)

Add equation (1) and (2)

47x + 31y + 31x + 47y = 63 + 15

78y + 78x = 78

78 (y + x) = 78

y + x = 1

y = 1 – x ……(3)

Subtract equation (1) and (2)

47x + 31y – 31x – 47y = 63 – 15

16x – 16y = 48

16 (x – y) = 48

x – y = 3 ……(4)

Substitute value of y from (3) in (4)

x – (1 – x) = 3

x – 1 + x = 3

2x = 4

x = 2

Put x = 2 in (3)

y = 1 – x

y = 1 – 2

y = – 1