Solve for x and y: x + y = a + b, ax - by = a2 - b2.

1.	Solve for x and y: x + y = a + b, ax - by = a2 - b2.
Answer» The given equations are x + y = a + b ………(i) ax - by = a² - b² ………(ii) From (i) y = a + b - x Substituting y = a + b - x in (ii), we get ax – b(a + b - x) = a² - b² ⇒ ax – ab - b² + bx = a² - b² ⇒x = a²+ab/a+b = a Now, substitute x = a in (i) to get a + y = a + b ⇒ y = b Hence, x = a and y = b

Answer»

The given equations are

x + y = a + b ………(i)

ax - by = a² - b² ………(ii)

From (i)

y = a + b - x

Substituting y = a + b - x in (ii), we get

ax – b(a + b - x) = a² - b²

⇒ ax – ab - b² + bx = a² - b²

⇒x = a²+ab/a+b = a

Now, substitute x = a in (i) to get

a + y = a + b

⇒ y = b

Hence, x = a and y = b

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