Question

Solve the system for a and b:
9 = ab^2
-72=ab^5

Answer 1

a =
`(9)/(4)` , b = - 2

Explanation:

Given the 2 equations

9 = ab² → (1)

- 72 = a
`b^(5)` → (2)

Divide (2) by (1)

`(-72)/(9)` =
`(ab^5)/(ab^2)`

- 8 = b³ ( take the cube root of both sides )

`\sqrt[3]{-8}` = b , that is

b = - 2

Substitute b = - 2 into (1) and solve for a

9 = a(- 2)² = 4a ( divide both sides by 4 )

`(9)/(4)` = a