Solve each of the following systems of equations by using the method of cross multiplication:
We have,
…(i)
…(ii)
Let 1/x = p and 1/y = q. Now,
From equation (i), p + q = 7
⇒ p + q – 7 = 0 …(iii)
From equation (ii), 2p – 3q = 17
⇒ 2p + 3q – 17 = 0 …(iv)
From equation (iii), we get a1 = 1, b1 = 1 and c1 = - 7
And from equation (iv), we get a2 = 2, b2 = 3 and c2 = - 17
Using cross multiplication,
⇒
⇒
⇒
⇒ and
⇒ p = 4 and q = 3
⇒ x = 1/4 and y = 1/3 [∵ p = 1/x and q = 1/y]
Thus, x = 1/4, y = 1/3