Solve the following pair of linear equations by elimination method. $ax b − b y a = a + b; a x − b y = 2 a b$

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x = − b and y = a

x = b and y = a

x = − b and y = − a

x = b and y = − a

answer is D.

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Detailed Solution

Given pairs of equations are:

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

Now to calculate the values of variable x and y.

Multiplying Eq . (i) by b a x − b 2 y a = a b + b 2 … (i i i) a x − b y = 2 a b

Subtracting Eq . (ii) from Eq . (iii), we get − b 2 y a + b y = a b + b 2 − 2 a b ⇒ − b y a + y = a + b − 2 a = b − a ⇒ y (a − b) = a (b − a) ⇒ y = − a

Putting the value of y, in equation (ii)

a x − b (− a) = 2 a b ⇒ a x = a b ⇒ x = b

Therefore, the values of variables are

x = b and y = − a

.
Hence, option (4) is correct.

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