Question

Solve the following linear equations :- ax-by=a²+b²
x+y=2a​

Answer 1

ax - by = a^2 + b^2 [Equation 1]

x + y= 2a  [Equation 2]  

Multiply Equation 2 by b  

=> bx + by= 2 ab [Equation 3]  

Add Equation 1 and 3  

⇒ ax + bx - by + by = a^2 + b^2 + 2ab  

⇒ (a + b)x = a^2 + b^2 + 2ab = (a + b)^2  [Using Identity we get]  

         

Put value x in Equation (2)  

(a + b) + y = 2a  

y = 2a - (a + b)  

y = 2a - a - b  

y = a - b

         

Answer 2

Answer:

ax-by=asquare+bsquare

x+y=2a

x(a+b)=a(b+a)

x=a