Solve for x and y:\(\frac{x}a+\frac{y}b=a + b\),\(\frac{x}{a^2}+\frac{

1.	Solve for x and y:\(\frac{x}a+\frac{y}b=a + b\),\(\frac{x}{a^2}+\frac{y}{b^2}=2\)
Answer» The given equations are \(\frac{x}a+\frac{y}b=a + b\)......(i) \(\frac{x}{a^2}+\frac{y}{b^2}=2\).....(ii) Multiplying (i) by b and (ii) by b² and subtracting, we get bx/a - b²x/a² = ab + b² - 2b² ⇒ ab− b^2/a² x = ab - b² ⇒x = (ab− b²)a²/ab −b² = a² Now, substituting x = a² in (i) we get a²/a + y/b = a + b ⇒ y/b = a + b – a = b ⇒y = b² Hence, x = a² and y = b² .

Solve for x and y:\(\frac{x}a+\frac{y}b=a + b\),\(\frac{x}{a^2}+\frac{y}{b^2}=2\)

Answer»

The given equations are

\(\frac{x}a+\frac{y}b=a + b\)......(i)

\(\frac{x}{a^2}+\frac{y}{b^2}=2\).....(ii)

Multiplying (i) by b and (ii) by b² and subtracting, we get

bx/a - b²x/a² = ab + b² - 2b²

⇒ ab− b^2/a² x = ab - b²

⇒x = (ab− b²)a²/ab −b² = a²

Now, substituting x = a² in (i) we get

a²/a + y/b = a + b

⇒ y/b = a + b – a = b

⇒y = b²

Hence, x = a² and y = b² .