SOLUTION: I'm suppose to solve this system of equations. I know substitution is the best way to try and solve it. 1000=ar^5 10=ar^3 I've already been given the solution, I just don't

Algebra ->  Equations -> SOLUTION: I'm suppose to solve this system of equations. I know substitution is the best way to try and solve it. 1000=ar^5 10=ar^3 I've already been given the solution, I just don't      Log On


   

Question 984933: I'm suppose to solve this system of equations. I know substitution is the best way to try and solve it.
1000=ar^5
10=ar^3
I've already been given the solution, I just don't know how to go about solving it.
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
1000 = ar^5
10 = ar^3
solve second equation for a
a = 10 / r^3
now substitute for a in first equation
1000 = (10 / r^3) * r^5
1000 = 10 * r^2
r^2 = 100
r = 10
**************************************
substitute for r in second equation
10 = a * (10^3)
a = 10 / 1000 = 1 / 100
**************************************
check our answers
1000 = (1 / 100) * 10^5
1000 = (1 / 100) * 100000
1000 = 1000
**************************************
1000 = 10 * 10^2
1000 = 10 * 100
1000 = 1000
our answers check, therefore
r = 10 and a = 1 / 100