If $2x + y = 18$ and $3x = 17 + y,$ what is the value of $x?$

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Thu Mar 24, 2022 1:04 pm

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If $2x + y = 18$ and $3x = 17 + y,$ what is the value of $x?$

A. 1
B. 4
C. 7
D. 9
E. 13

Answer: C

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Thu Mar 24, 2022 1:04 pm

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Brent@GMATPrepNow: 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: If $2x + y = 18$ and $3x = 17 + y,$ what is the value of $x?$

by Brent@GMATPrepNow » Fri Mar 25, 2022 6:03 am

Vincen wrote: ↑
Thu Mar 24, 2022 1:04 pm
If $2x + y = 18$ and $3x = 17 + y,$ what is the value of $x?$

A. 1
B. 4
C. 7
D. 9
E. 13

Answer: C

Source: Veritas Prep

Let's use the elimination method...

GIVEN:
2x + y = 18
3x = 17 + y

Take 3x = 17 + y and subtract y from both sides to get: 3x - y = 17

We now have:
2x + y = 18
3x - y = 17

ADD the two equations to get: 5x = 35
Solve: x = 7

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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