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

Question

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

Infinity Learn · Accepted Answer

The coordinates of the point of intersection of the given lines are

$(\frac{5}{3 + 4 m} - \frac{3 + 9 m}{3 + 4 m})$

It is given that the x-coordinate of this point is an integer

$∴ \frac{5}{3 + 4 m} is an integer$

$\begin{array}{l} \Rightarrow 3 + 4 m is a divisor of 5 \\ \Rightarrow 3 + 4 m = 1, 3 + 4 m = - 1, 3 + 4 m = 5, 3 + 4 m = - 5 \\ \Rightarrow m = - 1, - 2 [\begin{array}{c} ∵ 3 + 4 m = 1, 3 + 4 m = 5 do not \\ give integral values of m \end{array}] \end{array}$

Hence, there are two values of $m$ .

Equation of line in Straight lines

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The number of integer oalues of m, for which the x-coordinaie of the point of intersection of the lines $3 x + 4 y = 9$ and $y = m x + 1$ is also an integer

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Equation of line in Straight lines

Remember concepts with our Masterclasses.

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

Ready to Test Your Skills?

free study material

The number of integer oalues of m, for which the x-coordinaie of the point of intersection of the lines $3 x + 4 y = 9$ and $y = m x + 1$ is also an integer