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

Question

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

Skywalker18 · Answer

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

mahakmalik · Answer

I will also go with E.
As  X1/X2 = Y1/Y2
eql{C1/C2}

KS15 · Answer

Hello,

I think your answer is wrong,

1st equation should x-y=2
Using both, we have x=2.5, y=.5
Answer D

nipunjain14 · Answer

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

equation 2 : x+y = 3

thus exactly 1 set of solution

Ans:D

Why2settleForLess · Answer

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.

Skywalker18 · Answer

KS15  and  nipunjain14  - Thanks , edited !!

JeffTargetTestPrep · Answer

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

kannu44 · Answer

These are not parallel line . For parallel line slope has to be same . Answer should be D

saurabhsavant · Answer

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

Bunuel · Answer

Yes, that's correct, D is the answer.

sisirkant · Answer

Got tricked with the question

. Exactly one solution as x= 5/2 and y = ½

FlyingCycle · Answer

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.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards