If 3x + 2y = 7 and 2x – y = 7, what is the value of x ?

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If 3x + 2y = 7 and 2x – y = 7, what is the value of x ?

A. 0
B. 1
C. 7/5
D. 21/11
E. 3


OA E

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BTGmoderatorDC wrote:
Mon Apr 05, 2021 7:27 pm
If 3x + 2y = 7 and 2x – y = 7, what is the value of x ?

A. 0
B. 1
C. 7/5
D. 21/11
E. 3


OA E

Source: GMAT Prep
Let's use the elimination method to solve this system

Given:
3x + 2y = 7
2x – y = 7

Multiply both sides of the bottom equation by 2 to get the following equivalent equation:
3x + 2y = 7
4x – 2y = 14

Now add the two equations to get:
7x = 21

Solve: x = 3

Answer: E

Cheers,
Brent
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BTGmoderatorDC wrote:
Mon Apr 05, 2021 7:27 pm
If 3x + 2y = 7 and 2x – y = 7, what is the value of x ?

A. 0
B. 1
C. 7/5
D. 21/11
E. 3


OA E

Source: GMAT Prep
Solution:

If we subtract the second equation from the first, we have:

x + 3y = 0

3y = -x

y = -x/3

Substituting this in the first equation, we have:

3x + 2(-x/3) = 7

9x - 2x = 21

7x = 21

x = 3

Answer: E

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