The number of integral values of m such that | vedclass

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

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$2$

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(B) Given the lines $3x + 4y = 9$ and $y = mx + 1$.Substitute $y$ from the second equation into the first:$3x + 4(mx + 1) = 9$$3x + 4mx + 4 = 9$$(3 + 4m)x = 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 $\{1, -1, 5, -5\}$.Case $1$: $3 + 4m = 1$ $\Rightarrow 4m = -2$ $\Rightarrow m = -0.5$ (Not an integer)Case $2$: $3 + 4m = -1$ $\Rightarrow 4m = -4$ $\Rightarrow m = -1$ (Integer)Case $3$: $3 + 4m = 5$ $\Rightarrow 4m = 2$ $\Rightarrow m = 0.5$ (Not an integer)Case $4$: $3 + 4m = -5$ $\Rightarrow 4m = -8$ $\Rightarrow m = -2$ (Integer)The integral values of $m$ are $\{-1, -2\}$.Thus,the number of integral values of $m$ is $2$.

The number of integral values of $m$ such that the abscissa of the point of intersection of the lines $3x + 4y = 9$ and $y = mx + 1$ is also an integer,is

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