Chapter 8.10, Problem 2GP

(a)

To determine

The system of equations of:

There is twice number of patients as exciting patients at the doctor’s office.

The new patient’s number is $22$ more than existing patient’s numbers.

Answer to Problem 2GP

The system of equation is written as:

  $\begin{array}{l}y=2x\\ y=x+22\end{array}$

Explanation of Solution

Given:

Two conditions of problem:

There is twice number of new patients as exciting patients at the doctor’s office.

The new patient’s number is $22$ more than existing patient’s numbers.

Calculation:

Consider,

Existing numbers of patient: $x$

New patients: $y$

Now, need to write the conditions in the form of eqns.

  $y=2x$  .... (1)

  $y=x+22$  .... (2)

Conclusion:

The system of equation is written as:

  $\begin{array}{l}y=2x\\ y=x+22\end{array}$

(b)

To determine

The solution of the system by using the graphing method and meaning of the solution is to be needed.

Answer to Problem 2GP

The graphing solution of the set of eqn $\begin{array}{l}y=2x\\ y=x+22\end{array}$ is

  

Explanation of Solution

Given:

Two conditions of problem:

There is twice number of new patients as exciting patients at the doctor’s office.

The new patient’s number is $22$ more than existing patient’s numbers.

Calculation:

The equation is written as:

  $y=2x$  .... (1)

  $y=x+22$  .... (2)

Now, draw a graph these two eqns.

  

From graph:

Two graphing equations have the intersection point $\left(22,44\right)$ which is nothing but the solution of two eqns.

The meaning of solution is the new patients are $44$ which is double of existing number of patients $2$

Conclusion:

So, by using the graphing method the solution of the system of equations is $\left(22,44\right)$ which is point of intersection.