# Solve for x and y

We have,

x + y = a + b …(i)

ax – by = a2 – b2…(ii)

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

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

Recalling equations 1 & 2,

x + y = a + b [×b

ax – by = a2 – b2 bx + ax = ab + a2

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

x = a

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

Thus, substituting in equation (i), we get

a + y = a + b

y = b

Hence, we have x = a and y = b.

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