SOLUTION: If 3^a-b= 27 and 3^a+b=243 what is the value of a? I have the answer a-b=3 and a+b=5 and if you add the equations together 2a=8 so a =4 but don't understand why.

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons  -> Linear Equations Lesson -> SOLUTION: If 3^a-b= 27 and 3^a+b=243 what is the value of a? I have the answer a-b=3 and a+b=5 and if you add the equations together 2a=8 so a =4 but don't understand why.       Log On


   

Question 919202: If 3^a-b= 27 and 3^a+b=243 what is the value of a? I have the answer a-b=3 and a+b=5 and if you add the equations together 2a=8 so a =4 but don't understand why.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
a-b = 3 because 3^3 = 27, and the exponential function is 1-to-1.

Similarly a+b = 5 since 3^5 = 243.

Once you have a-b = 3, a+b = 5, you can solve for a and b.