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# If 4x − 3y = 13 and 5x + 2y = −1, then x =

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Math Expert
Joined: 02 Sep 2009
Posts: 44635
If 4x − 3y = 13 and 5x + 2y = −1, then x = [#permalink]

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11 Mar 2018, 21:17
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If 4x − 3y = 13 and 5x + 2y = −1, then x =

A. −3
B. −1
C. 1
D. 3
E. 5
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 44635
Re: If 4x − 3y = 13 and 5x + 2y = −1, then x = [#permalink]

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11 Mar 2018, 21:20
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If 4x − 3y = 13 and 5x + 2y = −1, then x = [#permalink]

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12 Mar 2018, 01:45
Bunuel wrote:
If 4x − 3y = 13 and 5x + 2y = −1, then x =

A. −3
B. −1
C. 1
D. 3
E. 5

We know that 4x - 3y = 13
To find the value of y: 3y = 4x - 13 -> y = $$\frac{4x - 13}{3}$$

Substuting the value of y in the second equation

$$5x + 2(\frac{4x - 13}{3}) = -1$$ -> $$5x + \frac{8x - 26}{3} = -1$$ -> $$15x + 8x - 26 = -3$$ -> $$23x=23$$

Therefore, the value of x is 1(Option C)
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Re: If 4x − 3y = 13 and 5x + 2y = −1, then x = [#permalink]

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12 Mar 2018, 05:58
1
KUDOS
Bunuel wrote:
If 4x − 3y = 13 and 5x + 2y = −1, then x =

A. −3
B. −1
C. 1
D. 3
E. 5

Question x = ?

4x − 3y = 13 -----(I) x 2

5x + 2y = −1------(II) x 3

we get

8x - 6y = 26-----(I)

15x + 6y = -3------(II)

Adding I & II we get

23x = 23

x = 1

(C)
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Re: If 4x − 3y = 13 and 5x + 2y = −1, then x = [#permalink]

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13 Mar 2018, 16:55
Bunuel wrote:
If 4x − 3y = 13 and 5x + 2y = −1, then x =

A. −3
B. −1
C. 1
D. 3
E. 5

We can multiply the first equation by 2 and the second by 3 and we have:

8x - 6y = 26

and

15x + 6y = -3

Adding the equations together, we have:

23x = 23

x = 1

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Joined: 26 Mar 2013
Posts: 1612
If 4x - 3y = 13 and 5x + 2y = -1, then x = [#permalink]

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15 Apr 2018, 20:34
If 4x - 3y = 13 and 5x + 2y = -1, then x =

A) -3
B) -1
C) 1
D) 3
E) 5
Intern
Joined: 15 Apr 2018
Posts: 2
Re: If 4x - 3y = 13 and 5x + 2y = -1, then x = [#permalink]

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15 Apr 2018, 20:54
2(4x-3y)=2(13)
3(5x+2y)=3(-1)

8x - 6y = 26
15x + 6y = -3

8x + 15x = 23
23x = 23
x = 1

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Math Expert
Joined: 02 Sep 2009
Posts: 44635
Re: If 4x − 3y = 13 and 5x + 2y = −1, then x = [#permalink]

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15 Apr 2018, 23:07
Mo2men wrote:
If 4x - 3y = 13 and 5x + 2y = -1, then x =

A) -3
B) -1
C) 1
D) 3
E) 5

Merging topics. Please refer to the discussion above.
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Joined: 26 Mar 2013
Posts: 1612
Re: If 4x − 3y = 13 and 5x + 2y = −1, then x = [#permalink]

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17 Apr 2018, 11:20
Bunuel wrote:
If 4x − 3y = 13 and 5x + 2y = −1, then x =

A. −3
B. −1
C. 1
D. 3
E. 5

Another way

4x − 3y = 13...........1

5x + 2y = −1...........2

--------------------------------sum both equations

9x - y = 12...............3

From equation 3: 9x is integer and multiple of 3 & 12 is multiple of 3.....So y must be integer multiple of 3 and more likely negative and x is positive (Review equation 2)

Let y =-3.............x = 1...We need to chelc the solution, then apply x & y equation 2.........Bingo

Re: If 4x − 3y = 13 and 5x + 2y = −1, then x =   [#permalink] 17 Apr 2018, 11:20
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