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

## Solution :

We have,

2x + 3y = 11        ….(1)

and 2x – 4y = -24        ……(2)

From equation (1), we have 2x = 11 – 3y

Substituting the value of 2x = 11 – 3y in (2), we get

11 – 3y – 4y = -24

-7y = -24 – 11

-7y = -35    $$\implies$$   y = 5

Putting y = 5 in equation (1), we get

2x + 3 $$\times$$ = 11

2x = 11 – 15

$$\implies$$  x = -$$4\over 2$$ = -2

Hence, x = -2  and y = 5

Now put x = – 2 and y = 5 in y = mx + 3, we get

5 = m(-2) + 3      $$\implies$$   -2m = 5 – 3

$$\implies$$   m = -$$2\over 2$$ = 1