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]