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

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(B) Given lines are: $3x + 4y = 9$  $(i)$ $y = mx + 1$  (ii) Substituting (ii) into $(i)$: $3x + 4(mx + 1) = 9$ $3x + 4mx + 4 = 9$ $x(3 + 4m) = 5$ $x

Vedclass · Accepted Answer

$2$

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(B) Given lines are: $3x + 4y = 9$  $(i)$ $y = mx + 1$  (ii) Substituting (ii) into $(i)$: $3x + 4(mx + 1) = 9$ $3x + 4mx + 4 = 9$ $x(3 + 4m) = 5$ $x = \frac{5}{3 + 4m}$ For $x$ to be an integer, $(3 + 4m)$ must be a divisor of $5$. The divisors of $5$ are $\pm 1, \pm 5$. 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). Thus, the possible integer values for $m$ are $-1$ and $-2$. The number of such integer values is $2$.

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

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