Chapter 9.6, Problem 12IP

a.

To determine

Tofind: the system of equations to represents solution.

Answer to Problem 12IP

Thesystem of equations is $x+y=5\text{ and }x-y=3$ .

Explanation of Solution

Given information:

The sum of two numbers is five and the difference of the numbers is three.

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

Since, the sum of numbers is five,

  $x+y=5$

And, the difference of the numbers is three.

  $x-y=3$

b.

To determine

To solve: the system of equations by graphing.

Answer to Problem 12IP

The solution of system of equations is $\left(4,1\right)$ .

Explanation of Solution

Given information:

The system of equation is $x+y=5\text{ and }x-y=3$ .

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,

$x$	$x+y=5$	$x-y=3$
$0$	$5$	$-3$
$2$	$3$	$-1$
$1$	$4$	$-2$

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 $\left(4,1\right)$ .