GMAT Math : Linear Equations, Two Unknowns

Study concepts, example questions & explanations for GMAT Math

Create An Account

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Linear Equations, Two Unknowns

Which equation is linear?

Possible Answers:

$x+\Pi y+ez=log(5)$

none of them are linear

$y=x^{2}-55x+1$

$\frac{y+8}{x-2}=x+6$

5x+7y-8yz=16

Correct answer:

$x+\Pi y+ez=log(5)$

Explanation:

Let's go through all of the answer choices.

1. $x+\Pi y+ez=log(5)$ : $\Pi$ and $e$ are both constants, so the equation is actually linear.

2. 5x + 7y - 8yz = 16: This is not linear because of the yz term.

3. $\frac{y+8}{x-2}=x+6$ : This can be transformed into y + 8 = (x + 6)(x - 2). Clearly when this is expanded, there will be an $x^{2}$ term, so this is not linear.

4. $y=x^{2}-55x+1$ : This is not linear either, also because of the $x^{2}$ term.

Report an Error

Example Question #2 : Linear Equations, Two Unknowns

Solve.

2x+3y=26

3x-4y=5

Possible Answers:

x=4; y=6

x=10; y=2

x=7; y=4

x=3; y=1

Correct answer:

x=7; y=4

Explanation:

Solve for in the first equation:

2x=26-3y

$x=13-\frac{3}{2}y$

Substitute into the second equation:

$3(13-\frac{3}{2}y)-4y=5$

$39-\frac{9}{2}y-4y=-34$

$-\frac{9}{2}y-4y=-34$

$-\frac{17}{2}y=-34$

$y=(-34)(-\frac{2}{17})=4$

Solve for .

2x+3(4)=26

2x+12=26

2x=14

x=7

Report an Error

Example Question #3 : Linear Equations, Two Unknowns

4x+y=27

2x-3y=-11

What is $x^{2} - y?$

Possible Answers:

Correct answer:

Explanation:

Solve the first equation to get y=27-4x

Substitute that into the second equation and get

2x-3*(27-4x) = -11

Solve the equation to get x=5 , then substitute that into the first equation to get y=7 .

Plugging those two values into $x^{2} - y$ , gives

$5^{2}-7=18$

Report an Error

Example Question #2 : Algebra

Solve the system of equations:

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

-4x+3y = 6

Possible Answers:

(0,2)

The system has no solution.

(3,4)

$(-1 \tfrac{1}{2}, 2)$

(3, 0)

Correct answer:

The system has no solution.

Explanation:

Multiply both sides of the first equation by 12:

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

$12 \cdot \left (\frac{x}{3}-\frac{y}{4} \right ) =12 \cdot 1$

$\frac{12}{1} \cdot \frac{x}{3}-\frac{12}{1} \cdot \frac{y}{4} =12$

$4x-\3y =12$

Now, add both sides of the two equations:

$4x-\3y =12$

$\underline{-4x+3y = 6}$

0=18

Since this is impossible, the system of equations is inconsistent and thus has no solution.

Report an Error

Example Question #1 : Linear Equations, Two Unknowns

$x^{2} - y ^{2} = 125$

x + y = 25

Give the solution set for .

Possible Answers:

$x = -15 \textrm{ or } x = 15$

Insufficient information is given to answer the question.

$x = -10 \textrm{ or } x = 10$

x = 10

x = 15

Correct answer:

x = 15

Explanation:

$x^{2} - y ^{2} = 125$

The expression on the left factors as the difference of squares:

(x+y )(x-y ) = 125

Since x + y = 25 , we can substitute:

25(x-y ) = 125

$25(x-y ) \div 25 = 125\div 25$

x-y = 5

We now have a system of linear equations to solve:

x-y = 5

$\underline{x + y = 25}$

$2x \;\;\;\;\;=30$

$2x \div 2 =30\div 2$

x = 15

Report an Error

Example Question #2 : Linear Equations, Two Unknowns

A company wants to ship some widgets. If the weight of the box plus one widget is 6 pounds, and the weight of the box plus two widgets is 10 pounds, then what is the weight of the box and the weight of the widget? Put the answer in an ordered pair such that the ordered pair is (box weight, widget weight).

Possible Answers:

$\left ( 2,4 \right )$

$\left ( 1,5 \right )$

$\left ( 4,2 \right )$

$\left ( 2,3 \right )$

$\left ( 2,2 \right )$

Correct answer:

$\left ( 2,4 \right )$

Explanation:

Let the weight of the box be represented by and the weight of the widget be represented by . Since the weight of the box plus the weight of one widget is 6 pounds, this can be represented by the equation

B+W=6

Since the weight of the box plus two widgets is 10 pounds, this can be represented by the equation

B+2W=10

We now have two equations and two unknowns and we can now solve for and . To do this we solve the first equation for and substitute it into the second equation. Solving the first equation for we get

B=6-W

Substituting this into the second equation we get

$(6-W)+2W=10\Rightarrow 6-W+2W=10\Rightarrow$

$6+W=10\Rightarrow W=10-6=4.$

Using W=4 and substituting it into the first equation we get

$B+4=6\Rightarrow B=6-4=2.$ So the weight of the box is 2 pounds and the weight of the widget is 4 pounds. This gives us the ordered pair $\left ( 2,4 \right )$ .

Report an Error

Example Question #1 : Algebra

Solve for when y=1.

7y+2x-8=9

Possible Answers:

Correct answer:

Explanation:

Plug in the given value and then isolate .

7y+2x-8=9

7(1)+2x-8=9

7+2x-8=9

2x-1=9

2x=9+1

2x=10

x=5

Report an Error

Example Question #5 : Algebra

Whats the value of when x=20 :

6y+7=17+7x

Possible Answers:

Correct answer:

Explanation:

6y+7=17+7x

6y+7=17+7(20)

6y+7=17+140

6y=17+140-7

6y=150

y=25

Report an Error

Example Question #1 : Linear Equations, Two Unknowns

Solve for :

2x+4y=10

Possible Answers:

x=-2y-5

x=-2y+5

x=2y+5

x=2y-5

Correct answer:

x=-2y+5

Explanation:

2x+4y=10

2x=10-4y

$x=\frac{10-4y}{2}$

x=-2y+5

Report an Error

Example Question #7 : Solving Linear Equations With Two Unknowns

$x^{2}+ y^{2} = 20$

x+ 2y = 10

What is ?

Possible Answers:

y = 8

y = 5

y = 2

y = 4

y = 10

Correct answer:

y = 4

Explanation:

From the second equation:

x+ 2y = 10

x+ 2y - 2y = 10 - 2y

x = 10 - 2y

Substitute into the first, then solve:

$\left ( 10-2y\right )^{2}+ y^{2} = 20$

$10^{2} - 2 \cdot 10 \cdot 2y + \left ( 2y \right )^{2} + y^{2} = 20$

$4y ^{2} + y^{2} - 40y + 100 = 20$

$5 y^{2} - 40y + 100 = 20$

$5 y^{2} - 40y + 100 - 20= 20 - 20$

$5 y^{2} - 40y + 80= 0$

$5 \left ( y^{2} - 8y + 16 \right )= 0$

$5 \left ( y - 4 \right )^{2}= 0$

y - 4 = 0

y = 4

Report an Error

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Biology Tutors in Seattle, GRE Tutors in San Diego, ISEE Tutors in Chicago, Biology Tutors in Phoenix, Spanish Tutors in New York City, English Tutors in Phoenix, Reading Tutors in Boston, Statistics Tutors in Miami, Computer Science Tutors in Philadelphia, Calculus Tutors in New York City

Popular Courses & Classes

GRE Courses & Classes in Phoenix, MCAT Courses & Classes in San Diego, GMAT Courses & Classes in Philadelphia, LSAT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Los Angeles, MCAT Courses & Classes in Houston, Spanish Courses & Classes in Seattle, ACT Courses & Classes in Boston, Spanish Courses & Classes in San Diego, MCAT Courses & Classes in Seattle

Popular Test Prep

ACT Test Prep in Boston, MCAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Boston, SAT Test Prep in San Francisco-Bay Area, GRE Test Prep in Denver, ISEE Test Prep in Washington DC, GRE Test Prep in Seattle, GMAT Test Prep in San Francisco-Bay Area, SAT Test Prep in San Diego, SAT Test Prep in Phoenix

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)

Email address:
Your name:
Feedback:

GMAT Math : Linear Equations, Two Unknowns

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Linear Equations, Two Unknowns

Example Question #2 : Linear Equations, Two Unknowns

Example Question #3 : Linear Equations, Two Unknowns

Example Question #2 : Algebra

Example Question #1 : Linear Equations, Two Unknowns

Example Question #2 : Linear Equations, Two Unknowns

Example Question #1 : Algebra

Example Question #5 : Algebra

Example Question #1 : Linear Equations, Two Unknowns

Example Question #7 : Solving Linear Equations With Two Unknowns

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details