Solve for $x$ and $y$ by substitution method $b x a − a y b + a + b = 0, b x − a y + 2 a b = 0$ .

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x = a and y =- b

x = -a and y = -b

x = a and y = b

x = -a and y = b

answer is D.

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Detailed Solution

Given equations are:

b x a − a y b + a + b = 0 … (i) b x − a y + 2 a b = 0 … (i i)

From Eq. (i),

a y b = b x a + a + b ⇒ a y = b 2 a x + a b + b 2

Putting in ay Eq. (ii),

b x − b 2 a x + a b + b 2 + 2 a b = 0 ⇒ b x − b 2 a x − a b − b 2 + 2 a b = 0 ⇒ b 1 − b a x = b 2 − a b ⇒ b (a − b) x = a b (b − a) ⇒ x = − a

Substituting the value of x, in equation (i),

a y = b 2 a (− a) + a b + b 2 ⇒ a y = a b ⇒ y = b

Therefore, the solution of the above equations is x = -a and y = b.
Hence, option (4) is correct.

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