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

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Aicharya · Accepted Answer

By solving $3 x+4 y=9, y=m x+1$, we get $x=\frac{5}{3+4 \mathrm{~m}}$
Now, $x$ is an integer, if $3+4 \mathrm{~m}=1,-1,5,-5$ $\therefore \quad \mathrm{m}=\frac{-2}{4}, \frac{-4}{4}, \frac{2}{4}, \frac{-8}{4}$. Since, $\mathrm{m}=\frac{-2}{4}, \frac{2}{4}$ do not give integral values of $m$. $\therefore \quad \mathrm{m}$ has two integer values.

The number of integer values of $m$, for which $x$-coordinate of the point of intersection of the lines $3…

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