solve the simultaneous equation 41/x -47/y =35 ; 47/x - 41/y =53
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call u = 1/x and v = 1/y
41 u - 4 7 v = 35 -- equation 1
47 u - 41 v = 53 -- equation 2
Multiply the first equation by 47 and second by 41 and then subtract equation 2 from equation 1, we get
41 * 47 u - 47 * 41 u - 47² v + 41² v = 47* 35 - 53 * 41
- 528 v = -528
v = 1
substituting in equation 1, we get ,
41 u - 47 = 35 => u = 82/41 = 2
1/x = u = 2 => x = 1/2
1/y = v = 1 => y = 1
41 u - 4 7 v = 35 -- equation 1
47 u - 41 v = 53 -- equation 2
Multiply the first equation by 47 and second by 41 and then subtract equation 2 from equation 1, we get
41 * 47 u - 47 * 41 u - 47² v + 41² v = 47* 35 - 53 * 41
- 528 v = -528
v = 1
substituting in equation 1, we get ,
41 u - 47 = 35 => u = 82/41 = 2
1/x = u = 2 => x = 1/2
1/y = v = 1 => y = 1
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47 35 4?
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