Q. 23 - Precalculus Enhanced with Graphing Utilities

Question

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.

$\frac{5}{y}+\frac{4}{y}=3$

Step-by-Step Solution

Answer

The required solution is $y=3$ and the graph of the solution is given below:

Step 1. Given information.

We have:

$\frac{5}{y}+\frac{4}{y}=3$

Step 2. Solve the equation algebraically.

The equation is $\frac{5}{y}+\frac{4}{y}=3$.

Multiply both sides by $y:$

$$\begin{gathered} \frac{5}{y}y+\frac{4}{y}y=3y \\ 5+4=3y \\ 9=3y \end{gathered}$$

Switch sides:

$3y=9$

Multiply both sides by $3:$

$$\begin{gathered} \frac{3y}{3}=\frac{9}{3} \\ y=3 \end{gathered}$$

Step 3. Verify the solution using a graphing utility.

The solution of the equation is $y=3.$

Draw the graph of the equation $\frac{5}{y}+\frac{4}{y}=3$ using the graphing utility: