Solve each of the following systems of equations by using the method of cross multiplication:

ax – by = 2ab.

We have,

…(i)

ax – by = 2ab …(ii)

By simplifying, we get

From equation (i),

…(iii)

From equation (ii),

ax – by – 2ab = 0 …(iv)

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

And from equation (iv), we get a₂ = a, b₂ = - b and c₂ = - 2ab

Using cross multiplication,

⇒

⇒

⇒

⇒ and

⇒ and

⇒ x = b and y = - a

Thus, x = b, y = - a