# Grantham University Algebra: System of Two Linear Equations Homework Question 1A system of equations: Has two or more equations with the same set of

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
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
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.