Solve $2x + 3y = 11$ and $2x - 4y = -24$ and hence find the value of $m$ for which $y = mx + 3$.

(M = -1) Given equations are:
$2x + 3y = 11$ $...(1)$
$2x - 4y = -24$ $...(2)$
From equation $(1)$,we express $x$ in terms of $y$:
$2x = 11 - 3y$
$x = \frac{11 - 3y}{2}$ $...(3)$
Substituting the value of $x$ from equation $(3)$ into equation $(2)$:
$2\left(\frac{11 - 3y}{2}\right) - 4y = -24$
$11 - 3y - 4y = -24$
$11 - 7y = -24$
$-7y = -24 - 11$
$-7y = -35$
$y = 5$
Now,substitute $y = 5$ into equation $(3)$ to find $x$:
$x = \frac{11 - 3(5)}{2} = \frac{11 - 15}{2} = \frac{-4}{2} = -2$
So,the solution is $x = -2$ and $y = 5$.
Now,substitute these values into the equation $y = mx + 3$ to find $m$:
$5 = m(-2) + 3$
$5 - 3 = -2m$
$2 = -2m$
$m = -1$