The number of integer values of m , for which the x -coordinate of the point of intersection of the lines 3 x + 4 y = 9 and y = m x + 1 is also an integer, is [2001]

Question

The number of integer values of $m$ , for which the $x$ -coordinate of the point of intersection of the lines $3 x + 4 y = 9$ and $y = m x + 1$ is also an integer, is [2001]

Smart Achievers · Accepted Answer

(1)

$3 x + 4 y = 9 and y = m x + 1 are two lines.$

On equating the value of $y$ from both equations to get the $x$ -coordinate of the point of intersection,

$3 x + 4 (m x + 1) = 9 \Rightarrow (3 + 4 m) x = 5$

$\Rightarrow x = \frac{5}{3 + 4 m}$

For $x$ to be an integer, $3 + 4 m$ should be a divisor of 5 i.e., $1, - 1, 5$ or $- 5 .$

$3 + 4 m = 1 \Rightarrow m = - \frac{1}{2}$ (not an integer)

$3 + 4 m = - 1 \Rightarrow m = - 1$ (integer)

$3 + 4 m = 5 \Rightarrow m = \frac{1}{2}$ (not an integer)

$3 + 4 m = - 5 \Rightarrow m = - 2$ (integer)

$∴$ $There are 2 integral values of m .$

Solution

Q.
The number of integer values of $m$ , for which the $x$ -coordinate of the point of intersection of the lines $3 x + 4 y = 9$ and $y = m x + 1$ is also an integer, is [2001]

1 2

2 0

3 4

4 1

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Solution

Q. The number of integer 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 [2001]

1 2

2 0

3 4

4 1

Want Us to Email you About Special Offers & Updates?

Q.
The number of integer values of $m$ , for which the $x$ -coordinate of the point of intersection of the lines $3 x + 4 y = 9$ and $y = m x + 1$ is also an integer, is [2001]