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

Question

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

Philoid · Accepted Answer

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

⇒ p = 1/a and q = 1/b

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