Given,

47x + 31y = 63    ...............1

31x + 47y = 15    ...............2

Multiply equation 1 by 31 and equation 2 by 47, we get

47 * 31x + 31 * 31y = 63*31    ...............3

31 * 47x + 47 * 47y = 15*47    ...............4

Subtraction equation 3 by 4, we get

    (47 * 31x + 31 * 31y) - (31 * 47x + 47 * 47y) = 63*31 - 15*47

=> 47 * 31x + 31 * 31y - 31 * 47x - 47 * 47y = 63*31 - 15*47

=>  31 * 31y - 47 * 47y = 63*31 - 15*47

=> 961y - 2209y = 1953 - 705

=> -1248y = 1248

=> y = -1248/1248

=> y = -1

From equation 1, we get

     47x + 31 * (-1) = 63

=> 47x - 31 = 63

=> 47x = 63 + 31

=> 47x = 94

=> x = 94/47

=> x = 2

Hence, x = 2, y = -1