Chapter 9.6, Problem 4GP

a.

To determine

Tofind: the system of equations to represents solution.

Answer to Problem 4GP

Thesystem of equations is $y=100+10x\text{ and }y=20x$ .

Explanation of Solution

Given information:

Amanda pays an one-time fee of $\$100$ and a monthly fee of $\$10$ to belong to a gym.

Maria pays only a monthly fee of $\$20$ to belong to her gym.

Calculation: to find the system of equations, let $x$ represents the number of months and $y$ represents the cost,

Since, Amanda pays an one-time fee of $\$100$ and a monthly fee of $\$10$ to belong to a gym.

  $y=100+10x$

And, Maria pays only a monthly fee of $\$20$ to belong to her gym.

  $y=20x$

b.

To determine

To solve: the system of equations by graphing.

Answer to Problem 4GP

The solution of system of equations is $\left(10,200\right)$ .

Explanation of Solution

Given information:

The system of equation is $y=100+10x\text{ and }y=20x$ .

Calculation: to find solution of the system of equations, first graph the both equations in the same coordinates plane,

To graph the equations, use the point plotting method,

$x$	$y=100+10x$	$y=20x$
$0$	$100$	$0$
$2$	$120$	$40$
$1$	$110$	$20$

By using above table, and joint the points smoothly,

The graph of the lines can be obtained as:

From the above graph it can be observed that the both lines intersect at the point $\left(10,200\right)$ .