Solve {l}{b(1)=15}{b(n)=b(n-1)(-3)}

$$\left. \begin{array} { l } { b ( 1 ) = 15 } \\ { b ( n ) = b ( n - 1 ) ( - 3 ) } \end{array} \right.$$

Solve for b, n

$$b=15$$

$$n=\frac{3}{4}=0.75$$

Solution Steps

Consider the first equation. Divide both sides by 1.

$$b=15$$

Consider the second equation. Insert the known values of variables into the equation.

$$15n=15\left(n-1\right)\left(-3\right)$$

Cancel out 15 on both sides.

$$n=\left(n-1\right)\left(-3\right)$$

Use the distributive property to multiply n-1 by -3.

$$n=-3n+3$$

Add 3n to both sides.

$$n+3n=3$$

Combine n and 3n to get 4n.

$$4n=3$$

Divide both sides by 4.

$$n=\frac{3}{4}$$

The system is now solved.

$$b=15 n=\frac{3}{4}$$