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# The system of equations has how many solutions?

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
The system of equations has how many solutions?  [#permalink]

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18 Oct 2018, 01:02
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Question Stats:

59% (00:58) correct 41% (01:33) wrong based on 41 sessions

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The system of equations has how many solutions?

3x - 6y = 9
2y - x - 3 = 0

A. None
B. Exactly 1
C. Exactly 2
D. Exactly 3
E. Infinitely many

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Joined: 29 Jan 2017
Posts: 6
Re: The system of equations has how many solutions?  [#permalink]

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18 Oct 2018, 01:18
IMO A.
Solving the two equations we get
x-2y=3 and x-2y=-3
There are no such values of x and y that satisfy both the equations.

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Joined: 13 Mar 2018
Posts: 24
GPA: 3.12
WE: Project Management (Other)
The system of equations has how many solutions?  [#permalink]

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18 Oct 2018, 01:28
Bunuel wrote:
The system of equations has how many solutions?

3x - 6y = 9
2y - x - 3 = 0

A. None
B. Exactly 1
C. Exactly 2
D. Exactly 3
E. Infinitely many

By rearranging and deducing two equations, we get

=>3x-6y=9
=>x-2y=3 ---- Equation 1

=>2y-x-3=0
=>x-2y+3=0
=>x-2y=-3 -------Equation 2

Now please note the following rules:
if two equation are given as :
ax+by=c
dx+ey=f

then if
a/d=b/e=c/f, then equations have infinite no. of solutions,
a/d not equal to b/e, then equations have a unique solution and
a/d=b/e not equal to c/f, then equations have no solution

Now applying above rules to equation 1 & 2, mentioned above
we get, 1/1=-2/-2 not equal to 3/-3
Hence, these equation have no solution. So, option A should be the correct option.
The system of equations has how many solutions?   [#permalink] 18 Oct 2018, 01:28
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