Question

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

Answer 1

Answer:

a = $\frac{9}{4}$ , b = - 2

Step-by-step explanation:

Given the 2 equations

9 = ab² → (1)

- 72 = a$b^{5}$ → (2)

Divide (2) by (1)

$\frac{-72}{9}$ = $\frac{ab^5}{ab^2}$

- 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 )

$\frac{9}{4}$ = a