Question

How do I solve this? What are the steps?

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).

3= a(b)⁰
75= a(b)²

Answer 1

Use the fact that any number raised to the 0 power is 1, to solve the first equation for the value of 'a'
Substitute the value of 'a' into the second equation and then solve b.

Explanation:

Given:

`3= a(b)^0`
`75= a(b)^2`

We know that `(b)^0 = 1`, therefore the first equation becomes:

`3= a(1)`

Solving for a:

`a=3`

Substituting into the second equation:

`75 = 3b^2`

Divide both sides by 3:

`b^2 = 25`

Use the square root on both sides. Remember that the square root has a negative and a positive value.

`b = -5 or b = 5`

There are two possible solutions `(3,5)` or `(3,-5)` and we are not given enough information to tell which is correct.