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