the solution of x+y=a-b and ax-by + a²+b² is
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Given equations are x + y = a – b …(i)
ax – by = a2 + b2 …(ii)
From eqn (i), x = a – b – y …(iii
On substituting x = a – b – y in eqn
(ii), we get ⇒ a(a – b – y) – by = a2 + b2 ⇒ a2 – ab – ay – by = a2 + b2 ⇒ – ab – y(a + b) = b2 ⇒ – y(a + b) = b2 + ab
Now, on putting y = – b in eqn (iii), we get ⇒ x = a – b – ( – b) ⇒ x = a Thus, x = a and y = – b.
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Answer:
Given equations are x + y = a – b …(i)
ax – by = a2 + b2 …(ii)
From eqn (i), x = a – b – y …(iii
On substituting x = a – b – y in eqn
(ii), we get ⇒ a(a – b – y) – by = a2 + b2 ⇒ a2 – ab – ay – by = a2 + b2 ⇒ – ab – y(a + b) = b2 ⇒ – y(a + b) = b2 + ab
Now, on putting y = – b in eqn (iii), we get ⇒ x = a – b – ( – b) ⇒ x = a Thus, x = a and y = – b.
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