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   ...................(1)
2x – 4y = – 24 ...................(2) 

From equation (1), we obtain 
x= \(\frac{11-3y}{2 }\)........................(3)

Substituting this value in equation (2), we obtain
2(\(\frac{11-3y}{2 }\)) - 4y = -24
11-3y -4y = -24
-7y = -35
y=5

Putting this value in equation (3), we obtain
x= \(\frac{11-3\times 5}{2}\) = \(-\frac{4}{2}\) =-2

Hence, x = −2, y = 5

Also,
y= mx + 3
5 =2m +3 
-2m = 2 
m=-1