Question

If ax+by= a^2- b^2 and bx+ay =0 then the value of x+y is?

Answer 1

Given ax+by=a^2-b^2 ; bx+ay=0
then x+y=?

Adding given equations
ax+by+bx+ay=a^2-b^2
(a+b)x+(a+b)y=a^2-b^2
(a+b)(x+y)=a^2-b^2
(a+b)(x+y)=(a+b)(a-b)
x+y=a-b

Answer 2

Given:

A pair of linear equations ax + by = 0 and bx + ay =$a^2-b^2$.

To Find:

The value of x+y.

Solution:

1.The given linear equations are bx + ay =0 and bx + ay =$a^2-b^2$.

2. Consider bx + ay = 0 as equation 1 and bx + ay =$a^2-b^2$ as equation 2.

3. Multiply equation 1 with b on both the sides,

=> b * (bx + ay) = 0 x b,

=> $b^2x + aby =0$, (Equation 3).

4. Multiply equation 2 with a on both the sides,

=> $a2x+ aby = a*(a^2-b^2)$, (Equation 4).

5. Subtract equation 3 from equation 4,

=>$x (a^2-b^2) +aby-aby = a(a^2-b^2)$,

=> x = a,

6. Substitute the value of a in equation 1,

=> ab + ay = 0,

=> y = -b.

7. Therefore the value of x + y is a + (-b).

Therefore, the value of x + y is a - b.