The number of integral values of m,for which | vedclass

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(A) Given the lines $3x + 4y = 9$ and $y = mx + 1$.Substitute $y$ from the second equation into the first:$3x + 4(mx + 1) = 9$$3x + 4mx + 4 = 9$$x(3 +

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$2$

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(A) Given the lines $3x + 4y = 9$ and $y = mx + 1$.Substitute $y$ from the second equation into the first:$3x + 4(mx + 1) = 9$$3x + 4mx + 4 = 9$$x(3 + 4m) = 5$$x = \frac{5}{3 + 4m}$For $x$ to be an integer,$(3 + 4m)$ must be a divisor of $5$. The divisors of $5$ are $\pm 1$ and $\pm 5$.Case $1$: $3 + 4m = 1 \implies 4m = -2 \implies m = -0.5$ (not an integer).Case $2$: $3 + 4m = -1 \implies 4m = -4 \implies m = -1$ (integer).Case $3$: $3 + 4m = 5 \implies 4m = 2 \implies m = 0.5$ (not an integer).Case $4$: $3 + 4m = -5 \implies 4m = -8 \implies m = -2$ (integer).The integral values of $m$ are $-1$ and $-2$. Thus,there are $2$ such values.

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

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