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# Which of the following is the number of solutions to the system of equ

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Math Expert
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Posts: 46272
Which of the following is the number of solutions to the system of equ [#permalink]

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14 Feb 2016, 10:51
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75% (hard)

Question Stats:

39% (01:05) correct 61% (01:03) wrong based on 187 sessions

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6x − 12 = 6y
5y + 5x = 15
Which of the following is the number of solutions to the system of equations shown above?

A. More than three
B. Exactly three
C. Exactly two
D. Exactly one
E. None

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Re: Which of the following is the number of solutions to the system of equ [#permalink]

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14 Feb 2016, 20:46
1
6x − 12 = 6y
=> 6x - 6y = 12
=> x- y =2 -- 1

5y + 5x = 15
=>x + y = 3 -- 2
From equation 1 and 2 , we get
2x = 5
=> x=2.5
y=.5
Therefore , the given system will have Exactly one solution
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Re: Which of the following is the number of solutions to the system of equ [#permalink]

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15 Feb 2016, 06:29
I will also go with E.
As $$X1/X2$$=$$Y1/Y2\neql{C1/C2}$$
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Re: Which of the following is the number of solutions to the system of equ [#permalink]

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15 Feb 2016, 12:00
Skywalker18 wrote:
6x − 12 = 6y
=> 6x + 6y = 12
=> x+y =2 -- 1

5y + 5x = 15
=>x + y = 3 -- 2
From equation 1 and 2 , we get
2=3 which is not possible
Therefore the given system of equations has no solutions
We can also view the given equation as 2 parallel lines .
a1/a2=b1/b2 ≠ c1/c2

Hello,

1st equation should x-y=2
Using both, we have x=2.5, y=.5
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Re: Which of the following is the number of solutions to the system of equ [#permalink]

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15 Feb 2016, 21:28
Skywalker18 wrote:
6x − 12 = 6y
=> 6x + 6y = 12
=> x+y =2 -- 1

5y + 5x = 15
=>x + y = 3 -- 2
From equation 1 and 2 , we get
2=3 which is not possible
Therefore the given system of equations has no solutions
We can also view the given equation as 2 parallel lines .
a1/a2=b1/b2 ≠ c1/c2

Shouldn't highlighted equation be :
6x-6y=12 => x-y = 2

equation 2 : x+y = 3

thus exactly 1 set of solution

Ans:D
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Joined: 07 Feb 2016
Posts: 6
Re: Which of the following is the number of solutions to the system of equ [#permalink]

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Updated on: 15 Feb 2016, 22:38
Converting it to y=mx+c will help, no?
We then have to check if these two are parallel. If they are not, we will have exactly one solution as equations themselves suggest that these are two lines.

Originally posted by Why2settleForLess on 15 Feb 2016, 22:00.
Last edited by Why2settleForLess on 15 Feb 2016, 22:38, edited 1 time in total.
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Re: Which of the following is the number of solutions to the system of equ [#permalink]

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15 Feb 2016, 22:04
KS15 and nipunjain14 - Thanks , edited !!
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Re: Which of the following is the number of solutions to the system of equ [#permalink]

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20 Apr 2017, 16:51
1
Bunuel wrote:
6x − 12 = 6y
5y + 5x = 15
Which of the following is the number of solutions to the system of equations shown above?

A. More than three
B. Exactly three
C. Exactly two
D. Exactly one
E. None

Let’s simplify both equations:

6x − 12 = 6y

6x - 6y = 12

x - y = 2

and

5y + 5x = 15

5x + 5y = 15

x + y = 3

Now if we add the two new equations x - y = 2 and x + y = 3, we would have 2x = 5 or x = 2.5. Since x + y = 3, we see that y must be 0.5. Thus we have exactly one solution - the ordered pair (2.5, 0.5).

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Re: Which of the following is the number of solutions to the system of equ [#permalink]

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26 Apr 2017, 10:08
These are not parallel line . For parallel line slope has to be same . Answer should be D
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Re: Which of the following is the number of solutions to the system of equ [#permalink]

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14 May 2017, 11:25
Bunuel wrote:
6x − 12 = 6y
5y + 5x = 15
Which of the following is the number of solutions to the system of equations shown above?

A. More than three
B. Exactly three
C. Exactly two
D. Exactly one
E. None

a lot of people r getting D as an answer, request expert advice....
from (i)....x-y=2
from (ii)...x+y=3

solving...x=5/2 and y=1/2
exactly one solution..

answer would b E i.e no solution if in the original statement no (i) its a (-) 6y on RHS
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Posts: 46272
Re: Which of the following is the number of solutions to the system of equ [#permalink]

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14 May 2017, 11:34
saurabhsavant wrote:
Bunuel wrote:
6x − 12 = 6y
5y + 5x = 15
Which of the following is the number of solutions to the system of equations shown above?

A. More than three
B. Exactly three
C. Exactly two
D. Exactly one
E. None

a lot of people r getting D as an answer, request expert advice....
from (i)....x-y=2
from (ii)...x+y=3

solving...x=5/2 and y=1/2
exactly one solution..

answer would b E i.e no solution if in the original statement no (i) its a (-) 6y on RHS

Yes, that's correct, D is the answer.
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Which of the following is the number of solutions to the system of equ [#permalink]

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22 May 2017, 13:14
Got tricked with the question . Exactly one solution as x= 5/2 and y = ½
Which of the following is the number of solutions to the system of equ   [#permalink] 22 May 2017, 13:14
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