Question

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

Answer 1

2x + 3y = 11……………………..(I)

2x – 4y = -24……………………… (II)

From equation (II), we get

x = $\frac{(11-3y)}{2}$ ………………….(III)

Substituting the value of x in equation (II), we get

2$\frac{(11-3y)}{2}$ – 4y = 24

11 – 3y – 4y = -24

-7y = -35

y = 5……………………..(IV)

Putting the value of y in equation (III), we get

x =$\frac{ (11-3×5)}{2}$ = $\frac{(-4)}{2}$ = -2

Hence, x = -2, y = 5

Also,

y = mx + 3

5 = -2m +3

-2m = 2

m = -1

Therefore the value of m is -1.