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

Question

Infinity Learn · Accepted Answer

The given lines are $$3x$$ $$+$$ $$4y$$ $$=$$ $$9$$ $$-------(1)$$ and y $$=$$ mx $$+$$ $$1$$ $$--------(2)$$ Solving (1) and (2), we get the $$x-coordinate$$ of the point of intersection as $$x=54m+3Since$$ $$x-coordinate$$ is an integer,∴    $$4m+3=$$±$$5$$     or     $$4m+3=$$±$$1Solving$$ these, only integer values of m are –$$1$$ and –$$2$$.∴   m $$=$$ –$$1$$, –$$2$$

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

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