solve by substitution and elimination method x/a + y/b=2 ax-by=a2-b2 Share with your friends Share 0 Manbar Singh answered this These equations can be written as given below:bx + ay = 2ab ..........1ax - by = a2 - b2 ..........2By substitution method :From 1, we get,ay = 2ab - bx⇒ y = 2ab - bxa ............3Substituting the value of y in 2, we get, ax - b 2ab - bxa = a2 - b2⇒ a2x - b 2ab - bx = a a2 - b2⇒ a2x - 2ab2 + b2x = a3 - ab2⇒ a2 + b2x = a3 - ab2 + 2ab2⇒ a2 + b2x = a3 + ab2⇒ a2 + b2x = a a2 + b2⇒ x = a a2 + b2a2 + b2 = a Substituting the value of x in 3, we get, y = 2ab - b × aa⇒ y = 2ab - aba = aba = bHence, the solution is x = a & y = b By elimination method :The given equations are:bx + ay = 2ab ...........1ax - by = a2 - b2 ...........2Multiplying 1 by a and 2 by b, we get,abx + a2y = 2a2b .............3abx - b2y = a2b - b3 ...........4Now subtracting 4 from 3, we get, a2y + b2y = 2a2b - a2b + b3⇒ a2 + b2y = a2b + b3⇒ a2 + b2y = b a2 + b2y = b a2 + b2a2 + b2 = bPutting the value of y in 1, we get, bx + a × b = 2ab⇒ bx + ab = 2ab⇒ bx = 2ab - ab⇒ bx = ab⇒ x = abb = aHence, the solution is x = a & y = b. 4 View Full Answer
