Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : Equations / Inequalities

Study concepts, example questions & explanations for Algebra 1

Create An Account

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #271 : Equations / Inequalities

Solve the following by substitution:

3x+y=2

y=x-2

Possible Answers:

x=1, y=1

No solution

x=-1, y=1

x=1, y=-1

x=-1, y=-1

Correct answer:

x=1, y=-1

Explanation:

To solve this equation you will plug the second equation straight into the first one by substituting what is written there for .

You will then get:

3x+(x-2)=2

From here you need to simplify by combining like terms:

4x-2=2

Bring the over by addition:

4x=4

Then divide both sides by to get:

x=1

You will then take this value of and plug it into either equation.

y=(1)-2=-1

Report an Error

Example Question #271 : Equations / Inequalities

Set A is composed of all multiples of 4 that are that are less than the square of 7. Set B includes all multiples of 6 that are greater than 0. How many numbers are found in both set A and set B?

Possible Answers:

Correct answer:

Explanation:

Start by making a list of the multiples of 4 that are smaller than the square of 7. When 7 is squared, it equals 49; thus, we can compose the following list:

$\text{4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, and 48}$

Next, make a list of all the multiples of 6 that are greater than 0. Since we are looking for shared multiples, stop after 48 because numbers greater than 48 will not be included in set A. The biggest multiple of 4 smaller that is less than 49 is 48; therefore, do not calculate multiples of 6 greater than 48.

$\text{6, 12, 18, 24, 30, 36, 42, and 48}$

Finally, count the number of multiples found in both sets. Both sets include the following numbers:

$\text{12, 24, 36, and 48}$

The correct answer is 4 numbers.

Report an Error

Example Question #1 : How To Find The Solution For A System Of Equations

A cube has a volume of 216 $cm^{3}$ . If its width is $3x^{2}$ , its length is -0.5x , and its height is $x^{3}$ +14 , find .

Possible Answers:

Correct answer:

Explanation:

Since the object in question is a cube, each of its sides must be the same length. Therefore, to get a volume of 216 $cm^{3}$ , each side must be equal to the cube root of 216 , which is cm.

We can then set each expression equal to .

The first expression (3x^2^ -6) can be solved by either or , but the other two expressions make it evident that the solution is x = -2 .

Report an Error

Example Question #1 : How To Find The Solution For A System Of Equations

3x + y = 8

2x + 4y = 12

Solve the system for and .

Possible Answers:

x = 2, y = 0

x = 10, y = -2

x = -4, y = 20

x = 2, y = 2

x = 3, y = -1

Correct answer:

x = 2, y = 2

Explanation:

The most simple method for solving systems of equations is to transform one of the equations so it allows for the canceling out of a variable. In this case, we can multiply 3x + y = 8 by (-4) to get -12x - 4y = -32 .

Then, we can add 2x + 4y = 12 to this equation to yield -10x = -20 , so x = 2 .

We can plug that value into either of the original equations; for example, 3(2) )+ y = 8 .

So, y = 2 as well.

Report an Error

Example Question #2 : How To Find The Solution For A System Of Equations

What is the solution to the following system of equations:

3x+5y = 15

3x+3y = 15

Possible Answers:

x=3,y=2

$x=3,y=\frac{6}{5}$

$x=2,y=\frac{13}{4}$

x = 5, y = 0

$x=\frac{1}{3},y=3$

Correct answer:

x = 5, y = 0

Explanation:

By solving one equation for , and replacing in the other equation with that expression, you generate an equation of only 1 variable which can be readily solved.

Report an Error

Example Question #3 : How To Find The Solution For A System Of Equations

Solve this system of equations for :

3x + 5y = 1

6x-y = 24

Possible Answers:

None of the other choices are correct.

$3\frac{1}{3}$

$2\frac{2}{3}$

$3\frac{2}{3}$

Correct answer:

$3\frac{2}{3}$

Explanation:

Multiply the bottom equation by 5, then add to the top equation:

6x-y = 24

$5 \left (6x-y \right ) =5\cdot 24$

30x-5y =120

$\underline{\textrm{\; } 3x + 5y = \; \; 1}$

$33x \;\;\;\;\;\; \; =121$

$x = \frac{121}{33} = \frac{11}{3} = 3 \frac{2}{3}$

Report an Error

Example Question #2 : How To Find The Solution For A System Of Equations

Solve this system of equations for :

3x + 5y = 23

6x-y = -9

Possible Answers:

$y = 2 \frac{1}{2}$

y = 5

y = 3

$y = 3 \frac{1}{2}$

None of the other choices are correct.

Correct answer:

y = 5

Explanation:

Multiply the top equation by :

3x + 5y = 23

$-2 \cdot \left (3x + 5y \right )= -2 \cdot 23$

$-6x -10y \right )= -46$

Now add:

$6x-\; \; y = -9$

$\underline{-6x -10y = -46}$

-11y = - 55

$-11y \div (-11) = -55\div (-11)$

y = 5

Report an Error

Example Question #4 : How To Find The Solution For A System Of Equations

Solve this system of equations for :

3x + 5y = 1

6x-y = 24

Possible Answers:

y = -2

$y = -1 \frac{3}{5}$

$y = -2 \frac{1}{5}$

$y = -1 \frac{4}{5}$

None of the other choices are correct.

Correct answer:

y = -2

Explanation:

Multiply the top equation by :

3x + 5y = 1

$-2 \cdot \left (3x + 5y \right )= -2 \cdot 1$

$-6x -10y \right )= -2$

Now add:

$\; \; 6x-\; \; \; y = 24$

$\underline{-6x -10y= -2} \right )$

-11y = 22

$-11y \div (-11) = 22\div (-11)$

y = -2

Report an Error

Example Question #3 : How To Find The Solution For A System Of Equations

Find the solution to the following system of equations.

a + 3b = 5

a-2b = 0

Possible Answers:

$a = 1,\ b = 1$

$a = 2,\ b = 1$

$a = 1,\ b = 2$

$a = 2,\ b = 2$

$a = 2,\ b = 3$

Correct answer:

$a = 2,\ b = 1$

Explanation:

a + 3b = 5

a-2b = 0

To solve this system of equations, use substitution. First, convert the second equation to isolate $\small a$ .

$a-2b = 0\rightarrow a=2b$

Then, substitute $\small 2b$ into the first equation for $\small a$ .

a + 3b = 5

(2b) + 3b = 5

Combine terms and solve for $\small b$ .

5b=5

b=1

Now that we know the value of $\small b$ , we can solve for $\small a$ using our previous substitution equation.

a=2b=2(1)=2

Report an Error

Example Question #5 : How To Find The Solution For A System Of Equations

Find a solution for the following system of equations:

$\left\{\begin{matrix} x-2y-1=3\\ -x+2y+2=5 \end{matrix}\right.$

Possible Answers:

$\left ( 8,2 \right )$

$\left ( 4,0 \right )$

no solution

infinitely many solutions

Correct answer:

no solution

Explanation:

When we add the two equations, the and variables cancel leaving us with:

1=8 which means there is no solution for this system.

Report an Error

View Algebra Tutors

Saarim
Certified Tutor

St Edwards University, Bachelor of Science, Mathematics.

View Algebra Tutors

Satweka
Certified Tutor

The University of Texas at Dallas, Master of Science, Biomedical Engineering.

View Algebra Tutors

Magdy
Certified Tutor

Cairo University, Egypt, Bachelor of Science, Electrical Engineering. New Mexico State University-Main Campus, Doctor of Phil...

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Physics Tutors in New York City, English Tutors in Chicago, Computer Science Tutors in Chicago, Biology Tutors in Denver, LSAT Tutors in Dallas Fort Worth, GMAT Tutors in San Diego, English Tutors in Phoenix, Algebra Tutors in Boston, Chemistry Tutors in Seattle, GMAT Tutors in Los Angeles

Popular Courses & Classes

ISEE Courses & Classes in Phoenix, SSAT Courses & Classes in New York City, LSAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Boston, MCAT Courses & Classes in Philadelphia, SAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Denver, ISEE Courses & Classes in San Diego, GRE Courses & Classes in Phoenix

Popular Test Prep

SAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Denver, GMAT Test Prep in Boston, SSAT Test Prep in Phoenix, SSAT Test Prep in Philadelphia, SSAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Philadelphia, MCAT Test Prep in Boston, ISEE Test Prep in Los Angeles, GRE Test Prep in Philadelphia

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Algebra 1 : Equations / Inequalities

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #271 : Equations / Inequalities

Example Question #271 : Equations / Inequalities

Example Question #1 : How To Find The Solution For A System Of Equations

Example Question #1 : How To Find The Solution For A System Of Equations

Example Question #2 : How To Find The Solution For A System Of Equations

Example Question #3 : How To Find The Solution For A System Of Equations

Example Question #2 : How To Find The Solution For A System Of Equations

Example Question #4 : How To Find The Solution For A System Of Equations

Example Question #3 : How To Find The Solution For A System Of Equations

Example Question #5 : How To Find The Solution For A System Of Equations

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: