BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

The system of equations has how many solutions?

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 10
Joined: Wed Aug 05, 2020 2:05 am
by GMATprofessional21 » Wed Aug 05, 2020 7:42 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

The system of equations has how many solutions?

3x − 6y = 9

2y − x − 3 = 0

A None
B Exactly 1
C Exactly 2
D Exactly 3
E Infinitely many
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

Re: The system of equations has how many solutions?

by Brent@GMATPrepNow » Wed Aug 05, 2020 9:09 am
GMATprofessional21 wrote: ↑
Wed Aug 05, 2020 7:42 am
 The system of equations has how many solutions?

3x − 6y = 9

2y − x − 3 = 0

A None
B Exactly 1
C Exactly 2
D Exactly 3
E Infinitely many
Given:
x - y = 3
2x = 2y + 6

Take 2x = 2y + 6 and divide both sides by 2 to get an EQUIVALENT equation x = y + 3
Now subtract y from both sides to get: to get another EQUIVALENT equation x - y = 3
Since this equation (x - y = 3) is identical to the other equation x - y = 3, we can be certain that ANY solution to x - y = 3 will also be a solution to x - y = 3

Since there are infinitely many solutions to x - y = 3, there will be infinitely many solutions to the entire SYSTEM.

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

Re: The system of equations has how many solutions?

by Brent@GMATPrepNow » Wed Aug 05, 2020 9:11 am
GMATprofessional21 wrote: ↑
Wed Aug 05, 2020 7:42 am
 The system of equations has how many solutions?

3x − 6y = 9

2y − x − 3 = 0

A None
B Exactly 1
C Exactly 2
D Exactly 3
E Infinitely many
Another approach is to begin solving the system (using the elimination method) and see what happens.

Given:
x - y = 3
2x = 2y + 6

Take bottom equation and divide both sides by 2 to get:
x - y = 3
x = y + 3

Take bottom equation and subtract y from both sides to get:
x - y = 3
x - y = 3

Now subtract the bottom equation from the top equation to get:
0x + 0y = 0
As we can see, this equation has infinitely many solutions.

Answer: E
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8152
Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members
Location: Los Angeles, CA
Thanked: 43 times

Re: The system of equations has how many solutions?

by Scott@TargetTestPrep » Mon Aug 10, 2020 10:32 am
GMATprofessional21 wrote: ↑
Wed Aug 05, 2020 7:42 am
 The system of equations has how many solutions?

3x − 6y = 9

2y − x − 3 = 0

A None
B Exactly 1
C Exactly 2
D Exactly 3
E Infinitely many
Solution:

Multiplying the second equation by 3, we have:

6y - 3x - 9 = 0

6y - 3x = 9

-3x + 6y = 9

Adding the equations together, we have:

0 = 18

Since 0 can’t be equal to 18, there are no solutions that satisfy the given system of equations.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1