Question

solve the following system of equation by elimination method equation X + y = a - b , ax - by = a2 + b2​

Answer 1

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

Step-by-step explanation:

Given : Equations x+y=a+bx+y=a+b and ax-by=a²-b²ax−by=a²−b²

To find : Solve the equations ?

Solution :

Let x+y=a+bx+y=a+b .......(1)

and ax-by=a²-b²ax−by=a²−b² ......(2)

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

a(a+b-y)-by=a²-b²a(a+b−y)−by=a²−b²

a²+ab-ay-by=a²-b²a²+ab−ay−by=a¹−b²

ab-ay-by=-b^2ab−ay−by=−b2

ab-y(a+b)=-b^2ab−y(a+b)=−b2

y(a+b)=ab+b^2y(a+b)=ab+b2

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.