Q. 13

# Solve each of the following systems of equations by using the method of cross multiplication: Where x ≠ 0 and y ≠ 0

We have, …(i) …(ii)

Let 1/x = p and 1/y = q. Now,

From equation (i), ap – bq = 0

ap – bq + 0 = 0 …(iii)

From equation (ii), ab2p – a2bq = (a2 + b2)

ab2p – a2bq – (a2 + b2) = 0 …(iv)

From equation (iii), we get a1 = a, b1 = - b and c1 = 0

And from equation (iv), we get a2 = ab2, b2 = - a2b and c2 = - (a2 + b2)

Using cross multiplication,      and  and p = 1/a and q = 1/b

Thus, x = a, y = b [ p = 1/x and q = 1/y]

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