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Pair of Linear Equations in Two Variables
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28/05/2021 10:43 am
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Solve the following pairs of equations by reducing them to a pair of linear equations:
5/(x-1) + 1/(y-2) = 2
6/(x-1) – 3/(y-2) = 1
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28/05/2021 10:45 am
(7x-2y)/ xy = 5
7/y – 2/x = 5 …………………..(i)
(8x + 7y)/xy = 15
8/y + 7/x = 15 ………………(ii)
Substituting 1/x = m in the given equation we get,
– 2m + 7n = 5
=> -2 + 7n – 5 = 0 ……..(iii)
7m + 8n = 15
=> 7m + 8n – 15 = 0 ……(iv)
By cross-multiplication method, we get,
m/(-105-(-40)) = n/(-35-30) = 1/(-16-49)
m/(-65) = n/(-65) = 1/(-65)
m/-65 = 1/-65
m = 1
n/(-65) = 1/(-65)
n = 1
m = 1 and n = 1
m = 1/x = 1 n = 1/x = 1
Therefore, x = 1 and y = 1