CPM Homework Help : INT3 Problem 4-108

Find values of $a$ and $b$ that make each system of equations true (i.e., solve each system). Be sure to show your work or explain your thinking clearly.

$6=a·b^0$
$24=a·b^2$
Hint (a):
Remember that $b^0=1$ .
Hint 2 (a):
You can use this fact to make the first equation $6=a$ , and then substitute $6$ for $a$ in the second equation.
More Help (a):
Solve for $b$ .
$24 = 6b^2$
$4=b^2$
$b = ±2$
Answer (a):
$a=6,\ b=±2$

$32=a·b^2$
$128=a·b^3$
Hint (b):
Here are three possible methods for solving.
Method 1(b):
Since $ab^3 = (ab^2)b$ , you can use substitution.
Then solve for $b$ and substitute to find $a$ .
$128 = (ab^2)b$ or $128 = 32b$
Method 2(b):
Solve the first equation for $a$ and substitute into the second equation. Then solve for $b$ and substitute to find $a$ .
$\frac{32}{b^2}=a$
$128=\frac{32}{b^2}(b^3)$
Method 3(b):
Since neither $a$ nor $b$ can equal $0$ , divide the second by the first.
$\frac{128=ab^3}{32=ab^2}$
$b=4$
Answer (b):
$a=2,\ b=4$