Question

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

Answer 1

`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`