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Tussy and Gustafson - Elementary Algebra 4/e (Homework)

James Finch

Math - Developmental, Fall 2010

Instructor: Dr. Friendly

Current Score: 3/25

Due: Saturday, November 6, 2010 23:00 EDT

About this Assignment

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Question

Points

1	2	3	4	5	6	7	8	9	10
2	0/8	0/2	0/2	0/2	1	0/3	0/1	0/2	0/2

Total

3/25

Description

Create your course assignments by selecting questions from our bank of 1500 end-of-section exercises, as well as enhanced interactive examples with videos.

While doing their homework, students can link to the relevant interactive examples from the book and work through them again and again for additional practice before answering the question.

Students can view and hear additional instruction through the 2-5 minute Watch It links. Students will also find helpful links to online excerpts from their textbook, online-live help, tutorials, and videos.

Read It - relevant textbook pages

- videos of worked examples

Practice It - interactive examples

Master It - tutorials

Chat About It - online, live help

In this assignment we present several textbook question types found in Chapter 4 on Systems of Linear Equations and Inequalities in Elementary Algebra 4/e by Alan S. Tussy and R. David Gustafson published by Brooks/Cole.

Instructions

This demo assignment allows many submissions and allows you to try another version of the same question for practice.

1. 2/2 points All Submissions Notes Question: TGElemAlg4 4.2.054.

Question part

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2/2

Solve the system by substitution.

{(6 x + y = -12 + 4 x - y, 3 x - y = 2 y + x -2)

x =

y =

Need Help?

2. 0/8 points All Submissions Notes Question: TGElemAlg4 4.2.E05.

Question part

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Submissions

1	2	3	4	5	6	7	8
0/1	0/1	0/1	0/1	0/1	0/1	0/1	0/1
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0/8

EXAMPLE 5

Solve the system: {( y/4 = - x/2 - 3/4, 2x - y = -1 + y - x)

Strategy

We will use properties of algebra to write each equation of the system in simpler form. Then we will use the substitution method to solve the resulting equivalent system.

Why

The first equation will be easier to work with if we clear it of fractions. The second equation will be easier to work with if we eliminate the variable terms on the right side.

Solution

We can clear the first equation of fractions by multiplying both sides by the LCD.

		x				3
		2				4

(

)

(

		x				3
		2				4

)

Multiply both sides by the LCD, 4. Don't forget the parentheses.

(

)

(

		x
		2

)

(

)

Distribute the multiplication by 4.

(1) y

- 2x - 3

Simplify. Call this result equation 1.

We can write the second equation of the system in standard Ax + By = C form by adding x and subtracting y from both sides.

(2)	2x - y	=	-1 + y - x
	2x - y + x - y	=	-1 + y - x + x - y
	3x - 2y	=	-1	Combine like terms. Call this equation 2.

Step 1: Equations 1 and 2 form an equivalent system, which has the same solution as the original one. To find x, we proceed as follows:

(1)	y = - 2x - 3		This is the substitution equation.
(2)	3x - 2y = -1

Step 2: To find x, substitute -2x - 3 for y in equation 2 and proceed as follows:

3x - 2y	=	-1
3x - 2(-2x - 3)	=	-1	Substitute -2x - 3 for y. Don't forget the parentheses.
3x + Enter an exact number. 1x + 6	=	-1	Distribute the multiplication by -2.
Enter an exact number. 2x + 6	=	-1	Combine like terms: 3 x + 4x = 7x.
Enter an exact number. 3x	=	-7	To isolate the variable term, 7x, subtract 6 from both sides.
x	=	Enter an exact number. 4	Divide both sides by 7. This is the x-value of the solution.

Step 3: To find y, we substitute -1 for x in equation 1.

y	=	-2x - 3
y	=	-2(-1) - 3	Substitute -1 for x.
y	=	Enter an exact number. 5 - 3	Do the multiplication.
y	=	Enter an exact number. 6	Subtract. this is the y-value of the solution.

Step 4: The solution is (-1, -1). Check it in the original system.

Self Check 5

Solve the system: {(y/20 = x/5 + 1/4, 14 x - 2 y = -15 + 2 y - x)

x =

y =

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3. 0/2 points All Submissions Notes Question: TGElemAlg4 4.4.036.

Question part

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0/2

In investing $5,500.00 of a couple's money, a financial planner put some of it into a savings account paying 6% annual interest. The rest was invested in a riskier mini-mall development plan paying 10% annually. The combined interest earned for the first year was $460.00. How much money was invested at each rate?
$ Your answer is incorrect.

put into savings account
$ Your answer is incorrect.

put into mini-mall

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4. –/2 points Notes Question: TGElemAlg4 4.4.022.

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0/2

To rehabilitate her knee, an athlete does leg extensions. Her goal is to regain a full 90° range of motion in this exercise. Use the information in the illustration to determine her current range of motion in degrees and the number of degrees of improvement she still needs to make. Let x = 5. (Figure is not drawn to scale.)

current	Enter an exact number. 1°
improvement	Enter an exact number. 2°

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5. –/2 points Notes Question: TGElemAlg4 4.2.076.

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0/2

Solve the system by substitution, if possible. If the system has no solution or infinitely many solutions, enter NO SOLUTION or INFINITELY MANY, as appropriate, in each answer box. (Do not use mixed numbers in your answer.)

${(4 x = 2 $y + 18$ + 3 x, 5 $x - 1$ = 3 y + 4 $x + 10$)$

x =
y =

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6. 1/1 points All Submissions Notes Question: TGElemAlg4 4.5.026.

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1/1

Graph the solutions of the system.

Flash Player version 10 or higher is required for this question.
You can get Flash Player free from Adobe's website.

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7. –/3 points Notes Question: TGElemAlg4 4.1.028.

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0/3

Solve the system of equations by graphing. If the system has no solution or infinitely many, so state.

Flash Player version 10 or higher is required for this question.
You can get Flash Player free from Adobe's website.

(If the system has no solution, enter NONE in each box. If there are infinitely many solutions, enter INFINITELY MANY in each box.)
x =
y =

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8. –/1 points Notes Question: TGElemAlg4 4.2.012.

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0/1

The system below was solved and it was found that b is 9 and a is 19. Write the solution as an ordered pair.

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9. –/2 points Notes Question: TGElemAlg4 4.3.072.

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0/2

Use the elimination method to solve the system. If there is no solution, or infinitely many solutions, so indicate. (Enter NO SOLUTION or INFINITELY MANY as appropriate in each answer box.)

$\left\{ \begin{array}{ll} & \dfrac{-{\color{red}15} x + y}{{\color{red}5}} = \dfrac{{\color{red}1}}{{\color{red}5}} \\ & {\color{red}15} x = y \end{array} \right.$

x =
y =

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10. –/2 points Notes Question: TGElemAlg4 4.1.006.

Question part

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0/2

We call equations with different graphs equations. Because equations are different forms of the same equation, they have the same graph.

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