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 $$+$$ I is also an integer, is

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Infinity Learn · Accepted Answer

The $$x-coordinate$$ of the point of intersection is $$3x$$ $$+$$ $$4$$ (mx+1) $$-$$ $$9$$  or (3+4m)x=5$$ or $$x=53+4mFor$$ x to be an integet,$$3$$ $$+$$ $$4m$$ should be a divisor of $$5$$, i.e., of $$1$$, $$-1$$, $$5$$, or $$-5$$. Hence, $$3+4m=1$$ or $$m=$$−$$12$$ $$(not$$ $$integer) $$3+4m=$$−$$1$$ or $$m=$$−$$1$$ (integer) $$3+4m=5$$ or $$m=12$$ (not$$ an $$integer) $$3+4m=$$−$$5$$ or $$m=$$−$$2$$ (integer) Hence, there are two integral values of m.

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 + I is also an integer, is

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