What are the steps to solving this problem so I can write them down?

Solve the following systems of equations. In other words, find values of a and b that make each system true. Write your answer as an ordered pair (a,b).
18=a(b)²
54=a(b)³

1 Answer
Feb 5, 2018

#a=2#
#b=3#

Explanation:

So we have:
#18=a(b)^2#
#54=a(b)^3#

Let's divide the second equation by 18 for both sides.

=>#54/18=(a(b)^3)/18#

Let's replace 18 with #a(b)^2# for the right side of the equation.

=>#54/18=(a(b)^3)/(a(b)^2)#

=>#3=(a*b*b*b)/(a*b*b)#

=>#3=(cancela*cancelb*cancelb*b)/(cancela*cancelb*cancelb)#

=>#3=b#

Since we know that #a(b)^2=18#, we can now solve for #a#.

#a(3)^2=18#

=>#9a=18#

=>#(9a)/9=18/9#

=>#a=2#