Question

x/a+y/b=2, ax-by=a²-b² solve for x and y by substitution method

Answer 1

Given x/a + y/b = 2.   ----- (*)

          x/a = 2 - y/b

          x = 2a - ay/b   ----- (1)


Given ax - by = a^2 - b^2

           a(2a - ay/b) - by = a^2 - b^2

           2a^2 - a^2y/b - by = a^2 - b^2

           a^2 - a^2y/b - by + b^2 = 0

           a^2 + b^2 = a^2y/b + by

           a^2 + b^2 = (a^2y + b^2y)/b

           b(a^2 + b^2) = (a^2 + b^2)y

             b = y.


substitute b = y in (*) we get

 x/a + y/b = 2

x/a + b/b = 2

x/a + 1 = 2

x/a = 1

x = a.



Hope this helps!