Grantham University Algebra: System of Two Linear Equations Homework

Description

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 (x) = 5x + 4 at (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 – 0.5x² 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) = 0.5^x 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

4^x = 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.