Chapter 6.1, Problem 26PPS

a.

To determine

Draw the graph of the two equations.

Explanation of Solution

Given:

It is given in the question that x is the number of years since and y is the percent of people paying bills, the following equations represent the percents of people writing checks to pa their bills and the percent of people paying their bills online. The equations are $y=-2x+24,y=6x+55$ .

Graph:

The graph for $y=-2x+24,y=6x+55$ is:

Interpretation: Here, put the both equation $y=-2x+24,y=6x+55$ in the graphing calculator, it gives the required graph.

In the above graph, it can be easily seen that the two graph intersect at $(-3.875,31.75)$ .

b.

To determine

Find the year at which the writing and the online payment were used equally. Check it.

Answer to Problem 26PPS

The both writing and the online payment were used equally nearly after $4$ years.

Explanation of Solution

Given:

It is given in the question that x is the number of years since and y is the percent of people paying bills, the following equations represent the percents of people writing checks to pay their bills and the percent of people paying their bills online. The equations are $y=-2x+24,y=6x+55$ . It is given in the question that the two graph gives the solution is $(-3.875,31.75)$ .

Concept Used:

In this, use the concept of linear equations by understanding the correct variable and constant .

Calculation:

Here, the solution is $(-3.875,31.75)$ .To check the answer enter it into the both equation.

  $\begin{array}{l}y=-2x+24\\ 31.75=-2(-3.875)+24\\ 31.75=7.75+24\\ 31.75=31.75\end{array}$

So, it is a solution for the first equation.Now check the second equation.

  $\begin{array}{l}y=6x+55\\ 31.75=6(-3.875)+55\\ 31.75=-23.25+55\\ 31.75=31.75\end{array}$

So, it is a solution for the second equation.

Hence, The both writing and the online payment were used equally nearly after $4$ years.Conclusion:

The both writing and the online payment were used equally nearly after $4$ years.