Let 'n' be the number of pairs of values of 'b' and 'c'

Question

Let 'n' be the number of pairs of values of 'b' and 'c' such that 3*x + b*y + c = 0 and c*x - 2*y + 12 = 0 have the same graph. Then n is:

A. 0
B. 1
C. 2
D. Finite but more than 2
E. greater than any finite number

gkumar08 · Answer

Ans is C
Since they have same graph so 
3/c = b/(-2)=c/12
So we get c=6,-6 b=1
So two set of values

Posted from my mobile device

ShaikhMoice · Answer

Why cant B be -1

Fdambro294 · Answer

It can:

There are two solution pairs for the answer:

1st solution pair for (b , c) = (-1 , 6)

2nd solution pair for (b , c) =. (+1 , -6)

Only these two solution pairs will make the lines represented by the linear equations coincident lines (I.e., the same line with infinite number of solutions)

KarishmaB · Answer

Though GMAT Focus does not have geometry, this part of co-ordinate geometry is included under graphing.

For the lines

3*x + b*y + c = 0 and
c*x - 2*y + 12 = 0

to be the same,  \frac{3}{c} = \frac{b}{-2} = \frac{c}{12} 
 c^2 = 36 
c = 6, -6
When c = 6, b = -1 and when c = -6, b = 1

Answer (C)

Kinshook · Answer

@twobagelsGiven: Let 'n' be the number of pairs of values of 'b' and 'c' such that 3*x + b*y + c = 0 and c*x - 2*y + 12 = 0 have the same graph.
Asked: Then n is:

3x + by + c = 0
cx - 2y + 12 = 0
have the same graph.

3/c = -b/2 = c/12
cˆ2 = 36; c = 6 or -6

Case 1: c=6
b = -c/6 = -1

Case 2: c=-6
b = -c/6 = 1

(b,c) = {(1,-6),(-1,6)} : 2 pair of values

IMO C

Elite097 · Answer

KarishmaB  can you explain this graph equation pls ? Why should they be equal

KarishmaB · Answer

This is related to the basics of linear simultaneous equations. If two equations represent the same line, then ax + by + c = 0 dx + ey + f = 0 a/d = b/e = c/f If the lines are parallel, then a/d = b/e but not equal to c/f If the lines are intersecting, a/d is not equal to b/e Here is a video explaining this and other relations: Linear Equations: https://youtu.be/Nh77CobN9mQ

Gmat750aspirant · Answer

3*x + b*y + c = 0 and
c*x - 2*y + 12 = 0

c = 6, -6
c = 6, b = -1 
c = -6, b = 1

Let 'n' be the number of pairs of values of 'b' and 'c'

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Let 'n' be the number of pairs of values of 'b' and 'c'

Prep Toolkit

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