body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

McGraw Hill Glencoe Algebra 1, 2012

MH

McGraw Hill Glencoe Algebra 1, 2012 View details

3. Elimination Using Addition and Subtraction

Continue to next subchapter

Exercise 32 Page 355

Practice makes perfect

a Let's begin by looking at the given table.

Catalogs	Number in $2014$	Growth Rate (number per year)
Online	$7440$	$1293$
Print	$3805$	$- 1364$

If we let

x

represent the number of years since

2014

and

y

represent the number of catalogs, we can write a system of linear equations to represent this situation. To do so we will write them in slope-intercept form.

y = m x + b

In this case the slope

m

is given by the growth rate and the number of catalogs in

2014

will be the

y -

b .

This is because we are taking into consideration the number of years since

2014 .

Let's write this information as a system of equations.

{y = 1293 x + 7740 y = - 1364 x + 3805 (I) (II)

Equation (I) represents the online catalogs and Equation (II) represents the printed catalogs.

b Since

y

and

y

have the same coefficient, we can use the Elimination Method to solve the system of equations. To do so, we will subtract Equation (II) from Equation (I).

{y = 1293 x + 7740 y = - 1364 x + 3805 (I) (II)

$(I):$ Subtract $(II)$

{y - y = 1293 x + 7740 - (- 1364 x + 3805) y = - 1364 x + 3805

▼

Solve Equation (I) for

x

$(I):$ Distribute $- 1$

{y - y = 1293 x + 7740 + 1364 x - 3805 y = - 1364 x + 3805

$(I):$ Add and subtract terms

{0 = 2657 x + 3935 y = - 1364 x + 3805

$(I):$ $LHS - 3935 = RHS - 3935$

{- 3935 = 2657 x y = - 1364 x + 3805

$(I):$ $LHS / 2657 = RHS / 2657$

{\frac{- 3 9 3 5}{2 6 5 7} = x y = - 1364 x + 3805

$(I):$ Rearrange equation

{x = - \frac{3 9 3 5}{2 6 5 7} y = - 1364 x + 3805

$(I):$ Use a calculator

{x = - 1.480993 \dots y = - 1364 x + 3805

$(I):$ Round to $2$ decimal place(s)

{x \approx - 1.48 y = - 1364 x + 3805

The

x -

variable is about

- 1.48 .

To find the

y -

variable, we will substitute

- 1.48

for

x

in Equation (II).

{x \approx - 1.48 y = - 1364 x + 3805

$(II):$ $x = - 1.48$

{x \approx - 1.48 y \approx - 1364 (- 1.48) + 3805

▼

Solve Equation (II) for

y

MultNegNegOnePar

$(II):$ $- a (- b) = a \cdot b$

{x \approx - 1.48 y \approx 2018.72 + 3805

$(II):$ Add terms

{x \approx - 1.48 y \approx 5823.72

The

y -

variable is about

5823.72 .

Therefore, the solution of the system of equations, which is the point of intersection of the two lines, is about

(- 1.48, 5823.72) .

c We are asked to analyze the solution in the context of the given situation. Since the

x -

variable represents the number of years since

2004,

it is not reasonable for it to be a negative number. Therefore, after the year

2004

there will never be a time when there is the same number of online and printed catalogs.

Subchapter links

Check Your Understanding p.353

H.O.T. Problems p.355

Standardized Test Practice p.356

Spiral Review p.356

Skills Review p.356