Question

ax - by = a2 +b2 x+y = 2a. solve it by Substituting Method​

Answer 1

x = (a + b) and y = (a – b).

Step-by-step explanation:

We have,

ax – by = a2 + b2 …(i)

x + y = 2a …(ii)

To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.

Lets multiply equation (ii) by b, so that variable y in both the equations have same coefficient.

Recalling equations (i) & (ii),

ax – by = a2 + b2

x + y = 2a [×b

⇒ ax + bx = a2 + b2 + 2ab

⇒ (a + b)x = (a + b)2

⇒ x = a + b

Substitute x = (a + b) in equations (i)/(ii), as per convenience of solving.

Thus, substituting in equation (ii), we get

a + b + y = 2a

⇒ y = 2a – a – b

⇒ y = a – b

Hence, we have x = (a + b) and y = (a – b).