Solve \(2x + 3y = 11\) and \(2x - 4y = -24\) and hence find the value of ‘m’ for which \(y = mx + 3\).

\(2x + 3y = 11\)...........(i)
=> \(2x - 4y = -24\)..............(ii)

Using equation (ii)
=> \(2x = -24 + 4y \)
=> \(x = -12 + 2y\).............(iii)

On substituting (iii) in (i):
=>\(2(-12 + 2y) + 3y = 11\)
=>\( -24 + 4y + 3y = 11\)
=>\( 7y = 35\)
=>\( y = 5\)...........(iv)

On substituting (iv) in (i):
=>\(2x + 3 (5) = 11\)
=>\(2x = 11 – 15 = -4\)
=>\(x = -2\)

So, the value of \(y = 5\) and \(x = -2\).

On substituting the values of x and y in \(y = mx + 3\),
=> \(5 = m (-2) + 3\)
=> \(5 = -2m + 3\)
=> \(-2m = 2\)
\(=> m = -1\)