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# 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 $$y = mx + 3$$,
=> $$5 = m (-2) + 3$$
=> $$5 = -2m + 3$$
=> $$-2m = 2$$
$$=> m = -1$$