System of Equations...1

[nycmathguy]

 

[MathLover1]

x-y=(a-b)/(a+b)..........eq.1
x+y=1.............eq.2
----------------------------------

x+y=1.............eq.2, solve for x

x=1-y.............eq.2a

substitute in eq.1

1-y-y=(a-b)/(a+b)..........eq.1, solve for y

(1-2y)=(a-b)/(a+b)

(1-2y)(a+b)=(a-b)
-2ay + a - 2by + b=a-b
-2ay + a - 2by + b-a+b=0
-2ay - 2by +2b=0
2b=2ay+2by
b=ay+by
b=(a+b)y

y=b/(a+b)

go to

x=1-y.............eq.2a, substitute y
x=1-b/(a+b)
x=((a+b)- b)/(a+b)
x=(a+b- b)/(a+b)
x=a/(a+b)

 

[nycmathguy]

x-y=(a-b)/(a+b)..........eq.1
x+y=1.............eq.2
----------------------------------

x+y=1.............eq.2, solve for x

x=1-y.............eq.2a

substitute in eq.1

1-y-y=(a-b)/(a+b)..........eq.1, solve for y

(1-2y)=(a-b)/(a+b)

(1-2y)(a+b)=(a-b)
-2ay + a - 2by + b=a-b
-2ay + a - 2by + b-a+b=0
-2ay - 2by +2b=0
2b=2ay+2by
b=ay+by
b=(a+b)y

y=b/(a+b)

go to

x=1-y.............eq.2a, substitute y
x=1-b/(a+b)
x=((a+b)- b)/(a+b)
x=(a+b- b)/(a+b)
x=a/(a+b)

A job well-done. I am very impressed.