Grantham University Algebra: System of Two Linear Equations Homework Question 1A system of equations: Has two or more equations with the same set of unknowns Has one equation and two unknowns Has two equations with different sets of unknowns Has more sets of unknowns than equations Question 2A system of two linear equations and two unknowns can be solved by: Elimination Substitution Graphing the equations All of the above Question 3A system of two linear equations and three unknowns can be solved by: Elimination Substitution Graphing the equations It cannot be solved Question 4A system of equations has as many equations as there are variables (unknowns). True FalseQuestion 5Solve these two equations by elimination, substitution or graphingEquation 1: x+y=1Equation 2: -2x+4y=6 X=-1/3, y = 4/3 X= 4/3, y = -1/3 X=1/3, y=4/3 X=-4/3, y-=1/3 Question 6For the following System of Equations, the Matrix Form included below is correct.2x+y+z=4 6y+5z=-33x5y-z=27 Matrix Form: True FalseQuestion 7The cost C (in millions of dollars) of removing p% of the industrial and municipal pollutants discharged into a river is given byAccording to this model, explain why or why not it is possible to remove 100% of the pollutants? SHOW YOUR WORK Question 8 The admission fee at the county fair is $2 for children and $4 for adults. On a certain day, 2000 people enter the fair and $5000 is collected. Using c as the variable to represent the number of children and a as the variable for adults, write a system of equations to determine how many children and how many adults attended. Note down this system of equations so that you can use it for the next question. SHOW YOUR WORK Question 9 Based on the system of equations you wrote in the previous problem, how many children attended the county fair that day? SHOW YOUR WORK Question 10Evaluate the function ƒ(x) = 5x + 4 at ƒ(0) 9 1 4 0 Question 11The profit P (in hundreds of dollars) that a company makes depends on the amount x (in hundreds of dollars) the company spends on advertising according to the model. P(x) = 230 + 40x – 0.5×2 What expenditure for advertising will yield a maximum profit? 40 0.5 230 20 Question 12 The concentration C (in mg/dl), of a certain antibiotic in a patient’s bloodstream is given by 50t/T^2+25 where t is the time (in hours) after taking the antibiotic. What is the concentration 10 hours after taking the antibiotic? SHOW YOUR WORK Question 13 Write the logarithmic equation in exponential form. log2 16 = 4 SHOW YOUR WORK Question 14Find the domain of the function: All real numbers All real numbers except x=3 All positive real numbers All real numbers except x=0 Question 15 pH is a measure of the hydrogen ion concentration of a solution. It is defined as the negative logarithm of the hydrogen ion concentration.The equation is: pH = – log [H+] If an acid has an H+ concentration of 10-7, find the pH? SHOW YOUR WORK Question 16 In order to join a movie streaming service, you pay a $75 annual fee, then $1.50 for each movie you stream. Which equation will allow you to determine the cost you will pay if you stream x number of movies? Select from the following equations and indicate the correct answer in the space below: 1st, 2nd, 3rd, or 4th. Question 17 Evaluate the function at the indicated value of x. Function: f(x) = 0.5x Value: x = 2 SHOW YOUR WORK Question 18Find the domain of the function Domain: all real numbers x except x=7 Domain: all real numbers x except x=6 Domain: all real numbers x Domain: all real numbers x except x = -6 Question 19 Express the following matrix as a system of equations: SHOW YOUR WORK Question 20 Solve for x. SHOW YOUR WORK 4x = 16 Question 21A system of equations that is represented graphically by two PARALLEL lines has _____ solutions 0 1 2 Infinite Question 22 Solve the following system using substitution. What does x equal? What does y equal? 2x + y = 9 3x – y = 16 Question 23 Write the following System of Equations in Matrix Form. Indicate which Matrix Form below is correct: 1st or 2nd. Question 1

A system of equations:

Has two or more equations with the same set of unknowns

Has one equation and two unknowns

Has two equations with different sets of unknowns

Has more sets of unknowns than equations

Question 2

A system of two linear equations and two unknowns can be solved by:

Elimination

Substitution

Graphing the equations

All of the above

Question 3

A system of two linear equations and three unknowns can be solved by:

Elimination

Substitution

Graphing the equations

It cannot be solved

Question 4

A system of equations has as many equations as there are variables (unknowns).

True

False

Question 5

Solve these two equations by elimination, substitution or graphing

Equation 1: x+y=1

Equation 2: -2x+4y=6

X=-1/3, y = 4/3

X= 4/3, y = -1/3

X=1/3, y=4/3

X=-4/3, y-=1/3

Question 6

For the following System of Equations, the Matrix Form included below is correct.

2x+y+z=4

6y+5z=-33x

5y-z=27

Matrix Form:

True

False

Question 7

The cost C (in millions of dollars) of removing p% of the industrial and municipal

pollutants discharged into a river is given by

According to this model, explain why or why not it is possible to remove 100% of the

pollutants? SHOW YOUR WORK

Question 8

The admission fee at the county fair is $2 for children and $4 for adults. On a

certain day, 2000 people enter the fair and $5000 is collected. Using c as the

variable to represent the number of children and a as the variable for adults,

write a system of equations to determine how many children and how many

adults attended. Note down this system of equations so that you can use it for

the next question. SHOW YOUR WORK

Question 9

Based on the system of equations you wrote in the previous problem, how

many children attended the county fair that day? SHOW YOUR WORK

Question 10

Evaluate the function ƒ(x) = 5x + 4 at ƒ(0)

9

1

4

0

Question 11

The profit P (in hundreds of dollars) that a company makes depends on the

amount x (in hundreds of dollars) the company spends on advertising according

to the model. P(x) = 230 + 40x – 0.5×2 What expenditure for advertising will yield

a maximum profit?

40

0.5

230

20

Question 12

The concentration C (in mg/dl), of a certain antibiotic in a patient’s bloodstream is given

by 50t/T^2+25 where t is the time (in hours) after taking the antibiotic. What is the

concentration 10 hours after taking the antibiotic? SHOW YOUR WORK

Question 13

Write the logarithmic equation in exponential form.

log2 16 = 4

SHOW YOUR WORK

Question 14

Find the domain of the function:

All real numbers

All real numbers except x=3

All positive real numbers

All real numbers except x=0

Question 15

pH is a measure of the hydrogen ion concentration of a solution. It is defined as the

negative logarithm of the hydrogen ion concentration. The equation is:

pH = – log [H+]

If an acid has an H+ concentration of 10-7, find the pH? SHOW YOUR WORK

Question 16

In order to join a movie streaming service, you pay a $75 annual fee, then

$1.50 for each movie you stream. Which equation will allow you to determine

the cost you will pay if you stream x number of movies? Select from the

following equations and indicate the correct answer in the space

below: 1st, 2nd, 3rd, or 4th.

Question 17

Evaluate the function at the indicated value of x.

Function: f(x) = 0.5x Value: x = 2 SHOW YOUR WORK

Question 18

Find the domain of the function

Domain: all real numbers x except x=7

Domain: all real numbers x except x=6

Domain: all real numbers x

Domain: all real numbers x except x = -6

Question 19

Express the following matrix as a system of equations: SHOW YOUR WORK

Question 20

Solve for x. SHOW YOUR WORK

4x = 16

Question 21

A system of equations that is represented graphically by two PARALLEL lines has

_____ solutions

0

1

2

Infinite

Question 22

Solve the following system using substitution. What does x equal? What

does y equal?

2x + y = 9

3x – y = 16

Question 23

Write the following System of Equations in Matrix Form. Indicate which Matrix Form

below is correct: 1st or 2nd.

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