We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : How to find the solution for a system of equations

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 #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 #161 : Expressions & Equations

3x + y = 8

2x + 4y = 12

Solve the system for and .

Possible Answers:

x = 3, y = -1

x = -4, y = 20

x = 2, y = 0

x = 2, y = 2

x = 10, y = -2

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 #31 : Equations / Solution Sets

What is the solution to the following system of equations:

3x+5y = 15

3x+3y = 15

Possible Answers:

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

x=3,y=2

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

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

x = 5, y = 0

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 #271 : Equations / Inequalities

Solve this system of equations for :

3x + 5y = 1

6x-y = 24

Possible Answers:

$3\frac{1}{3}$

None of the other choices are correct.

$3\frac{2}{3}$

$2\frac{2}{3}$

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 #32 : Equations / Solution Sets

Solve this system of equations for :

3x + 5y = 23

6x-y = -9

Possible Answers:

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

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

None of the other choices are correct.

y = 3

y = 5

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 #162 : Expressions & Equations

Solve this system of equations for :

3x + 5y = 1

6x-y = 24

Possible Answers:

y = -2

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

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

None of the other choices are correct.

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

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 #33 : Equations / Solution Sets

Find the solution to the following system of equations.

a + 3b = 5

a-2b = 0

Possible Answers:

$a = 1,\ b = 1$

$a = 1,\ b = 2$

$a = 2,\ b = 2$

$a = 2,\ b = 3$

$a = 2,\ b = 1$

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 #34 : Equations / Solution Sets

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:

infinitely many solutions

$\left ( 4,0 \right )$

no solution

$\left ( 8,2 \right )$

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

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

Solve for :

4x+3=9x+12-2x

Possible Answers:

None of the other answers

Correct answer:

Explanation:

First, combine like terms to get 4x+3=7x+12 . Then, subtract 12 and from both sides to separate the integers from the 's to get -9=3x . Finally, divide both sides by 3 to get x=-3 .

Report an Error

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

We have two linear functions:

y=-4x+8

y=3x-5

Find the coordinate at which they intersect.

Possible Answers:

$(x,y)=\left(\frac{5}{2},\frac{1}{7} \right )$

$(x,y)=\left(14,7 )$

$(x,y)=\left(\frac{13}{7},\frac{4}{7} \right )$

$(x,y)=\left(-\frac{13}{7},-\frac{1}{9} \right )$

none of these

Correct answer:

$(x,y)=\left(\frac{13}{7},\frac{4}{7} \right )$

Explanation:

We are given the following system of equations:

y=-4x+8

y=3x-5

We are to find and . We can solve this through the substitution method. First, substitute the second equation into the first equation to get

3x-5=-4x+8

Solve for by adding 4x to both sides

3x+4x-5=-4x+4x+8

7x-5=8

Add 5 to both sides

7x-5+5=8+5

7x=13

Divide by 7

$\frac{7x}{7}=\frac{13}{7}$

$x=\frac{13}{7}$

So $x=\frac{13}{7}$ . Use this value to find using one of the equations from our given system of equations. I think I'll use the first equation (can also use the second equation).

y=-4x+8

$y=-4\left (\frac{13}{7} \right )+8$

$y=-\frac{52}{7}+8$

$y=-\frac{52}{7}+\frac{56}{7}$

$y=\frac{4}{7}$

So the two linear functions intersect at

$(x,y)=\left(\frac{13}{7},\frac{4}{7} \right )$

Report an Error

View Algebra Tutors

Emory
Certified Tutor

Davidson College, Bachelor in Arts, Arabic.

View Algebra Tutors

Jennifer
Certified Tutor

Baylor University, Bachelor of Science, Biochemistry. Stephen F Austin State University, Master of Science, Chemistry.

View Algebra Tutors

Kaltra
Certified Tutor

University of Florida, Bachelor of Science, Biomedical Engineering.

All Algebra 1 Resources

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

Popular Subjects

Spanish Tutors in Denver, SSAT Tutors in Los Angeles, English Tutors in New York City, French Tutors in Chicago, Spanish Tutors in Washington DC, English Tutors in San Francisco-Bay Area, Spanish Tutors in Boston, Statistics Tutors in Miami, Chemistry Tutors in Dallas Fort Worth, SAT Tutors in Seattle

Popular Courses & Classes

GRE Courses & Classes in Denver, SAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Chicago, ACT Courses & Classes in Los Angeles, GMAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Chicago, ACT Courses & Classes in New York City, SSAT Courses & Classes in New York City, GRE Courses & Classes in San Diego, SSAT Courses & Classes in Chicago

Popular Test Prep

MCAT Test Prep in Washington DC, LSAT Test Prep in Seattle, GRE Test Prep in Denver, GMAT Test Prep in Chicago, GMAT Test Prep in Philadelphia, SAT Test Prep in Denver, GMAT Test Prep in Miami, SAT Test Prep in Phoenix, LSAT Test Prep in Denver, SSAT Test Prep in Atlanta

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 : How to find the solution for a system of equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

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

Example Question #161 : Expressions & Equations

Example Question #31 : Equations / Solution Sets

Example Question #271 : Equations / Inequalities

Example Question #32 : Equations / Solution Sets

Example Question #162 : Expressions & Equations

Example Question #33 : Equations / Solution Sets

Example Question #34 : Equations / Solution Sets

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

Example Question #1 : 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: