if √ax-√by=b-a and √bx-√ay=0 then value of x,y is - Maths - Pair of Linear Equations in Two Variables

Question

if √ax-√by=b-a and √bx-√ay=0 then value
of x,y is

Manbar Singh · Accepted Answer

The given equations are:ax - by = b - a 1bx - ay = 0 2Put a = p and
b = q in given equations, we get,px - qy = q2 - p2 3qx - py = 0
4Adding 3 and 4 we get, px + qx - qy - py = q2 - p2⇒x p + q -
y p + q = q2 - p2⇒ p + q x - y = q2 - p2⇒ x - y = -p2 -
q2p + q⇒ x - y = -p + q p - qp + q⇒ x - y = -p -
q⇒ x - y = -p + q 5

Subtracting 4 from 3 we get, px - qx - qy + py = q2 - p2⇒ x p
- q + y p - q = q2 - p2⇒ p - q x + y = q2 - p2⇒ x + y =
-p2 - q2p - q⇒ x + y = -p + q p - qp - q⇒ x + y = - p +
q⇒ x + y = -p - q 6Adding 5 and 6 we get, 2x = -2p⇒ x=
-p⇒ x = -a as p = aSubtracting 5 from 6 we get, 2y =
-2q⇒ y = -q⇒ y = -b as q = bHence, x = -a and y = -b