Question

x+y=a+b and ax-by=a*a-b*b then find x and y​

Answer 1

Step-by-step explanation:

Equations x+y=a+bx+y=a+b and ax-by=a^2-b^2ax−by=a

2

−b

2

To find : Solve the equations ?

Solution :

Let x+y=a+bx+y=a+b .......(1)

and ax-by=a^2-b^2ax−by=a

2

−b

2

......(2)

Substitute x from (1) in equation (2),

a(a+b-y)-by=a^2-b^2a(a+b−y)−by=a

2

−b

2

a^2+ab-ay-by=a^2-b^2a

2

+ab−ay−by=a

2

−b

2

ab-ay-by=-b^2ab−ay−by=−b

2

ab-y(a+b)=-b^2ab−y(a+b)=−b

2

y(a+b)=ab+b^2y(a+b)=ab+b

2

y(a+b)=b(a+b)y(a+b)=b(a+b)

y=by=b

Substitute y in equation (1),

x+b=a+bx+b=a+b

x=a+b-bx=a+b−b

x=ax=a

Therefore, The solution of the equations is x=a and y=b.