x+y=a+b

ax-by=a^2-b^2

Solve for x and y

Asked by ananyachandra90 | 14th Jun, 2019, 11:44: AM

Expert Answer:

begin mathsize 16px style straight x space plus space straight y space equals space straight a space plus space straight b space.... space left parenthesis straight i right parenthesis
ax space minus space by space equals space straight a squared space minus space straight b squared space space space.... space left parenthesis ii right parenthesis
Multiply space left parenthesis straight i right parenthesis space by space straight b comma space we space get
straight b straight x space plus space by space equals space ab space plus space straight b squared space.... space left parenthesis iii right parenthesis
Adding space equation space left parenthesis ii right parenthesis space and space left parenthesis iii right parenthesis comma space we space get
ax space plus space bx space equals space ab space plus space straight a squared
rightwards double arrow space straight x left parenthesis straight a space plus space straight b right parenthesis space equals space straight a left parenthesis straight a space plus space straight b right parenthesis
rightwards double arrow space straight x space equals space straight a
Put space straight x space equals space straight a space in space left parenthesis straight i right parenthesis comma space we space get
straight a space plus space straight y space equals space straight a space plus space straight b
rightwards double arrow space straight y space equals space straight b space
end style

Answered by Yasmeen Khan | 14th Jun, 2019, 02:15: PM