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Taking 1/x = u, the given equation becomes
4u + 5y = 7………(i)
3u + 4y = 5………(ii)
Subtracting (ii) from (i), we get
4u + 5y – (3u + 4y) = 7 – 5 ⇒ u + y = 2 ⇒
u = 2 – y………(iii)
Using (iii) in (i), 4(2 – y) + 5y = 7
⇒ 8 – 4y + 5y = 7 ⇒ y = -1
Putting y = -1 in (iii), we find u u = 2 – (-1) ⇒ u = 3 ⇒ x = 1/u = 13/13
Hence, the solution for the given system of equations is x = 13/13 and y = -1
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