Q. 204.0( 21 Votes )
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Answer :
Given: … (1)
ax - by = 2ab … (2)
Multiplying by ab to (1) and a to (2), we get
a2x – b2y = a2b + ab2 … (3)
a2x – aby = 2a2b … (4)
Subtracting equation (4) from equation (3),
(a2x – a2x) + ( - aby) – ( - b2y) = (2a2b - a2b) – ab2
⇒ - aby + b2y = a2b – ab2
⇒ by(b – a) = ab(a – b)
⇒ y = b(b – a) / ab(a – b)
⇒ y = - a
Substitute y value in (2),
ax – b( - a) = 2ab
⇒ ax + ab = 2ab
⇒ ax = ab
⇒ x = b
The solution is x = b and y = - a.
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