Chapter 9.6, Problem 11IP

a.

To determine

Tofind: the system of equations to represents solution.

Answer to Problem 11IP

Thesystem of equations is $y=50+5x\text{ and }y=90-5x$ .

Explanation of Solution

Given information:

Ling starts out with $50$ baseball cards and plans to collect $5$ per month. Jonathan starts out with $90$ baseball cards and plans to sell $5$ per month.

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

Since, Ling starts out with $50$ baseball cards and plans to collect $5$ per month

  $y=50+5x$

And, Jonathan starts out with $90$ baseball cards and plans to sell $5$ per month.

  $y=90-5x$

b.

To determine

To solve: the system of equations by graphing.

Answer to Problem 11IP

The solution of system of equations is $\left(4,70\right)$ .

Explanation of Solution

Given information:

The system of equation is $y=50+5x\text{ and }y=90-5x$ .

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,

$x$	$y=50+5x$	$y=90-5x$
$0$	$50$	$90$
$2$	$60$	$80$
$1$	$55$	$85$

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 $\left(4,70\right)$ .