Call Now to Set Up Tutoring:

(888) 888-0446

GRE Subject Test: Math : Solving Systems of Equations

Study concepts, example questions & explanations for GRE Subject Test: Math

Create An Account

All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Solving Systems Of Equations

2y=6x+4

y=7x-2

Solve the system of equations.

Possible Answers:

x=4, y=8

$x=-8, y=\frac{1}{2}$

x=1, y=5

x=-1, y=3

x=-2, y=-3

Correct answer:

x=1, y=5

Explanation:

The easiest way to solve this question is to use substitution. Since y=7x-2 you can replace y for 7x-2 in the other equation.

You should have

2(7x-2)=6x+4 .

Distribute the 2 to the parentheses.

14x-4=6x+4

Add 4 to both sides of the equation.

14x=6x+8

Subtract 6x from both sides.

8x=8

Divide by 8 to get x.

x=1

Put 1 back in to either equation for x to solve for y.

y=3(1)+2

y=5

Report an Error

Example Question #2 : Solving Systems Of Equations

-3x+2y=19

-3x-19=2y

Solve the system of equations.

Possible Answers:

$x=-6\frac{1}{3}, y=0$

$x=\frac{1}{4}, y=-2\frac{1}{5}$

$x=3, y=-4\frac{1}{5}$

$x=-1, y=-4\frac{1}{3}$

$x=-\frac{1}{5}, y=2\frac{1}{4}$

Correct answer:

$x=-6\frac{1}{3}, y=0$

Explanation:

First task is to solve at least one of the equations for y.

-3x+2y=19

Move -3x to the other side by adding 3x to both sides.

2y=3x+19

Divide by 2 to all the terms in the equation.

$y=\frac{3}{2}x+\frac{19}{2}$

Plug this value for y into the other equation.

$-3x-19=2(\frac{3}{2}x+\frac{19}{2})$

Distribute the 2.

-3x-19=3x+19

Add 3x to both sides.

-19=6x+19

Subtract 19 from both sides of the equation.

-38=6x

Divide by 6.

$x=-6.33 or -6\frac{1}{3}$

Plug this back in for x in either equation.

-3(-6.33)+2y=19

19+2y=19

2y=0

y=0

Report an Error

Example Question #291 : Algebra

Solve each system of equations.

y = 2x-16

y + 3x = 9

Possible Answers:

(5,6)

(5,-6)

(-5,-6)

(-5,6)

Correct answer:

(5,-6)

Explanation:

To solve this system of equations, you are given the value of .

y = 2x - 16

The second equation is y + 3x = 9

So you put the value of into the second equation.

2x-16 + 3x = 9

Combine like terms.

5x -16 = 9

Add to both sides of the equation.

5x - 16 + 16 = 9 + 16

5x = 25

Divide both sides by .

$\frac{5x}{5} = \frac{25}{5}$

x = 5

Substitute the value of x in one of the equations to get the value of y.

y = 2(5) - 16

y = 10-16

y = -6

(5,-6) is the correct answer.

Report an Error

Example Question #292 : Algebra

Solve the system of equations.

x + y = 5

2x - 3y =5

Possible Answers:

(1,4)

(4, 1)

(4, -1)

(-4, -1)

Correct answer:

(4, 1)

Explanation:

x + y = 5

2x-3y = 5

To cancel out the terms, multiply x + y = 5 by

-2x - 2y = -10

Then add:

2x-3y = 5

______________________

-5y = -5

y = 1

Plug the value of which is into one of the equations to get the value of .

x + 1 = 5

x+1-1 = 5 - 1

x = 4

(4,1) is the correct answer.

Report an Error

Example Question #121 : Linear Algebra

Solve each system of equations.

y = 6x

y = x-15

Possible Answers:

(-18,-3)

(18,3)

(3,18)

(-3,-18)

Correct answer:

(-3,-18)

Explanation:

Using the substitution method, set the two systems of equations equal to each other.

6x = x-15

Isolate the variable by subtracting from both sides of the equation.

6x-x = x-x-15

5x = -15

$\frac{5x}{5} = \frac{-15}{5}$

x = -3

To get the value of , substitute the value of in one of the equations.

y = 6(-3)

y = -18

(-3,-18) is the correct answer.

Report an Error

Example Question #4 : Solving Systems Of Equations

Solve each system of equations.

y = -x + 6

y = 2x-3

Possible Answers:

(-3,-3)

(-3,3)

(3,3)

(3,-3)

Correct answer:

(3,3)

Explanation:

Using the substitution method, set both systems of equations equal to each other.

-x + 6 = 2x - 3

Isolate the variable by adding to both sides of the equation.

-x + x + 6 = 2x + x -3

6 = 3x - 3

Add to both sides.

9 = 3x

Divide both sides by 3.

$\frac{9}{3} =\frac{3x}{3}$

3 = x

To get the value of y, substitute the value of x in one of the equations.

2 (3) - 3 = 6 - 3 = 3

y = 3

(3,3) is the correct answer.

Report an Error

Example Question #3 : Solving Systems Of Equations

Solve the systems of equations.

-5x + 10 y = 60

-4x + 16y = 32

Possible Answers:

(-2,-16)

(-16,-2)

(-2,16)

(16,2)

Correct answer:

(-16,-2)

Explanation:

In order to eliminate the terms, first multiply the first equation by -4.

-4 (-5x+10y) = (-4) 60

20x - 40y = -240

Then multiply the second equation by

5 (-4x + 16y) = 5 (32)

-20 x +80y = 160

This will now eliminate the terms when added together.

20x - 40y = -240

+ -20 x +80y = 160

_________________________

40y = -80

Divide both sides by 40.

y = -2

Now substitute the value of which is -2, to get the value of in one of the the two original equations.

-5x-20 = 60

Add to both sides of the equation.

-5x -20 + 20 = 60 + 20

-5x = 80

Divide both sides by -5.

$80 \div -5 = -16$

x = -16

(-16,-2) is the correct answer.

Report an Error

Example Question #2 : Solving Systems Of Equations

Solve this system of equations:

y = -5x +2

y = 3x-14

Possible Answers:

(2,8)

(8,2)

(2,-8)

(-8,2)

Correct answer:

(2,-8)

Explanation:

Set both equations equal to each other and solve.

-5x + 2 = 3x - 14

Add to both sides of the equation.

-5x + 5x + 2 = 3x + 5x - 14

2 = 8x - 14

Add to both sides of the equation.

2+14 = 8x-14+14

16 = 8x

Divide both sides by 8.

x = 2

Plug the value of the variable into one of the equations to get the value of

-5(2) + 2 = y

-10 +2 =-8

y = -8

(2,-8) is the correct answer for this system of equations.

Report an Error

Example Question #6 : Solving Systems Of Equations

Solve this system of equations:

3.5x + 2.5y = 38

1.5x -7.5y = -18

Possible Answers:

(-4,8)

(4,8)

(-8,4)

(8,4)

Correct answer:

(8,4)

Explanation:

To solve this system of equations, multiply the first equation by .

3 (3.5x + 2.5y) =38 (3)

10.5x +7.5y = 114

Now add the two equations together to remove the terms.

10.5x +7.5y = 114

+ 1.5x -7.5y = -18

_____________________________

12.0x = 96

Divide both sides by .

$96\div12 = 8$

x = 8

Plug the value of the variable, which is into one of the equations.

3.5(8) + 2.5y = 38

28 + 2.5y = 38

Subtract from both sides of the equation.

28-28 + 2.5y = 38-28

2.5y = 10

Divide both sides by 2.5

y = 4

(8,4) is the correct answer for this system of equations.

Report an Error

Example Question #1 : Solving Systems Of Equations

Solve this system of equations:

$-\frac{1}{2}x - \frac{1}{4}y =3$

$-\frac{1}{3}x +\frac{1}{6}y = 2$

Possible Answers:

(6,0)

(0,-6)

(-6,0)

(0,6)

Correct answer:

(-6,0)

Explanation:

To solve this system of equations:

$-\frac{1}{3}x +\frac{1}{6}y = 2$

Multiply the first equation by and the second equation by .

$4 (-\frac{1}{2}x -\frac{1}{4}y) = 3(4)$

-2x -y =12

$-6 (-\frac{1}{3}x+\frac{1}{6} y) = (-6) 2$

2x-y = -12

Add these two equations; this will remove the terms.

-2x -y =12

+ 2x-y = -12

___________________

-2y = 0

y = 0

To get the value of , plug the value of , which is into one of the equations.

2x -y = -12

2x - 0 = -12

2x = -12

Divide both sides by

$\frac{2x}{2} = \frac{-12}{2}$

x = -6

(-6,0) is the correct answer for this system of equations.

Report an Error

View Tutors

Magdy
Certified Tutor

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

View Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

View Tutors

Joseph
Certified Tutor

Bank Street College of Education , Master's/Graduate, Early Childhood and Childhood General Education.

All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Statistics Tutors in Miami, ISEE Tutors in Miami, MCAT Tutors in Miami, LSAT Tutors in Boston, Math Tutors in Philadelphia, English Tutors in Miami, Algebra Tutors in Philadelphia, Physics Tutors in San Diego, English Tutors in San Francisco-Bay Area, Biology Tutors in New York City

Popular Courses & Classes

GMAT Courses & Classes in Houston, ISEE Courses & Classes in Miami, LSAT Courses & Classes in Denver, ACT Courses & Classes in Washington DC, GMAT Courses & Classes in Washington DC, SAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Houston, SSAT Courses & Classes in Denver, SAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Boston

Popular Test Prep

SSAT Test Prep in Miami, ACT Test Prep in Boston, GRE Test Prep in New York City, LSAT Test Prep in Atlanta, LSAT Test Prep in Washington DC, ACT Test Prep in Washington DC, SSAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Washington DC, ISEE Test Prep in Phoenix, MCAT Test Prep in Boston

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

GRE Subject Test: Math : Solving Systems of Equations

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #1 : Solving Systems Of Equations

Example Question #2 : Solving Systems Of Equations

Example Question #291 : Algebra

Example Question #292 : Algebra

Example Question #121 : Linear Algebra

Example Question #4 : Solving Systems Of Equations

Example Question #3 : Solving Systems Of Equations

Example Question #2 : Solving Systems Of Equations

Example Question #6 : Solving Systems Of Equations

Example Question #1 : Solving Systems Of Equations

All GRE Subject Test: Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: