Question

ax - by = a^2 + b ^ 2 , x + y = 2a ​

Answer 1

$\bf\huge\textbf{\underline{\underline{According\:to\:the\:Question}}}$  

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]  

$\bf\huge{\implies x = \dfrac{(a+b)^2}{a+b} = a + b}$          

Put value x in Equation (2)  

(a + b) + y = 2a  

y = 2a - (a + b)  

y = 2a - a - b  

y = a - b

$\bf\huge\bf\huge{\boxed{\bigstar{{y = a-b}}}}$          

Answer 2

2 answers · Mathematics

Answers

ax-by= a^2+b^2----@1

x+y= 2a------------@2

Multiply @2 with b

=> bx + by= 2 ab--------@3

Add @1+ @3

ax - by = a2 + b2

bx + by= 2 ab

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

=> (a + b) x= a^2 + b^2 + 2ab = (a + b)^2 ----as per identity

=> x = (a + b)^2 / (a +b) = a + b

using x in @2

(a +b) + y = 2a

y= 2a - (a + b)

Opening brackets

y = 2a - a - b

y = a - b

Hope this helps. All you need to know is the identity => (a + b)^2 = a^2 + 2ab + b^2

To check if your ans is correct use the value of x and y in @1 in the L.H.S. and check the R.H.S. and see if the answer matches.