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

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Bunuel
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Which of the following is the number of solutions to the system of equ [#permalink] New post   14 Feb 2016, 10:51
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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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D
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Skywalker18
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Re: Which of the following is the number of solutions to the system of equ [#permalink] New post   14 Feb 2016, 20:46
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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
Answer D
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Re: Which of the following is the number of solutions to the system of equ [#permalink] New post   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] New post   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

Answer E


Hello,

I think your answer is wrong,

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

Answer E



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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Why2settleForLess
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Re: Which of the following is the number of solutions to the system of equ [#permalink] New post   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] New post   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] New post   20 Apr 2017, 16:51
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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).

Answer: D
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Re: Which of the following is the number of solutions to the system of equ [#permalink] New post   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] New post   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..
D should b trhe answer

answer would b E i.e no solution if in the original statement no (i) its a (-) 6y on RHS
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Re: Which of the following is the number of solutions to the system of equ [#permalink] New post   14 May 2017, 11:34
Expert Reply
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..
D should b trhe answer

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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sisirkant
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Which of the following is the number of solutions to the system of equ [#permalink] New post   22 May 2017, 13:14
Got tricked with the question :). Exactly one solution as x= 5/2 and y = ½
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Re: Which of the following is the number of solutions to the system of equ [#permalink] New post   03 Jan 2021, 00:49
6x -6y =12
=> y = x -2

5y = -5x + 15
=> y = -x +3

slopes are 1 and -1 = lines are perpendicular to each other. Therefore they will have just one common point.
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Re: Which of the following is the number of solutions to the system of equ [#permalink]
03 Jan 2021, 00:49
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