Question

The lines y=x and y=mx cross at the point P. What is the sum of the positive integer values of m for which the coordinates of P are also positive integers?

( If it helps,the options are :
A-5
B-7
C-3
D-10
E-8 )

Answer 1

Answer:

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Step-by-step explanation:

The number of integral values of m, for which the x-coordinate of the point of intersection of the lines 3x+4y=9 and y=mx+1 is also an integer, is

A

2

B

0

C

4

D

1

Answer

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Correct option is

A

2

By solving both equations for x coordinate, we get

mx+1=

4

9−3x

⇒4mx+4=9−3x

Or, 3x+4mx+4=9

Or, x=5/(3+4m)

Since x has to be an integer, possible values of x are 5,−5,1,−1 for which,

the denominator on R.H.S. has to be 1,−1,5,−5 respectively.

Now, 3+4m=1,implies m=−0.5

3+4m=−1, implies m=−1

3+4m=5, implies m=0.5

3+4m=−5, implies m=−2.

Hence, two integral values of m are possible.